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Conversion of degree to radian angles P-1

Welcome to our comprehensive guide on converting trigonometric sexagesimal measures degree to radian angles. As an SEO expert in the realm of mathematics and education, we strive to provide you with a clear and concise breakdown of this fundamental concept.

Trigonometry forms the foundation of various disciplines, from engineering and physics to architecture and astronomy. In the trigonometric system, angles were historically measured using the sexagesimal system, which divides a circle into 360 degrees. Each degree is further divided into 60 minutes, and each minute is divided into 60 seconds, resulting in a precise representation of angles.

However, in modern mathematical applications and computations, radian measurement has gained widespread acceptance due to its inherent advantages. Radians measure angles based on the radius of a circle, which offers a direct correlation between arc length and angle measurement, making it more suitable for calculus and advanced mathematical analysis.

In this guide, we will take you through a step-by-step process of converting degree to radian angles, equipping you with the necessary skills to navigate between these two systems effortlessly.

Our expert team has crafted this guide with simplicity and clarity in mind. We will provide intuitive explanations of degree to radian angles, illustrative examples of degree to radian angles, and practical tips of degree to radian angles to ensure you grasp the conversion process effectively. Whether you are a student seeking to understand trigonometry concepts better or a professional looking to refresh your knowledge, this guide is tailored to meet your needs.

Our content is structured to cater to various learning styles, as we believe that understanding mathematical concepts should be accessible to everyone. We’ll walk you through converting common degree to radian angles, explore the relationship between degree to radian angles, and demonstrate the significance of radian measurement in calculus.

Additionally, our guide will address the most frequently asked questions, dispel common misconceptions, and offer practical applications of radians in real-world scenarios. By the end of this guide, you will possess a firm grasp of converting trigonometry sexagesimal measures into radians and appreciate the importance of this conversion in mathematical problem-solving.

We are committed to providing valuable, informative, and well-optimized content to ensure this guide reaches and helps as many learners as possible. So, whether you are a student, educator, or just a curious mind, join us on this learning journey as we demystify the world of trigonometry and radians.

In this post, we will express the following trigonometry sexagesimal measures of angles in Radian. In second part we will solve trigonometry angles in Radian into sexagesimal system.

The Matrix: A Quick Review 01

Question Answers of conversion of degree to radian angles

convert degree to radian
Question 01(i): 75^{\circ}

30^{\circ}=30^{\circ} \times \frac{\pi}{180} radian =\frac{\pi}{6} radian

Question 01(ii): 45^{\circ}

45^{\circ}=45^{\circ} \times \frac{\pi}{180} radian = \frac{\pi}{4} radian

Question 01(iii): 60^{\circ}

60^{\circ}=60^{\circ} \times \frac{\pi}{180} radian = \frac{\pi}{3} radian

Question 01(iv): 75^{\circ}

75^{\circ}=75^{\circ} \times \frac{\pi}{180} radian =5 \frac{\pi}{12} radian

Question 01(v): 90^{\circ}

90^{\circ}=90^{\circ} \times \frac{\pi}{180} radian =\frac{\pi}{2} radian

Question 01(vi): 105^{\circ}

105^{\circ}=105^{\circ} \times \frac{\pi}{180} radian =\frac{7 \pi}{12} radian

Question 01(vii): 120^{\circ}

120^{\circ}=120^{\circ} \times \frac{\pi}{180} radian =\frac{2 \pi}{3} radian

Question 01(viii): 120^{\circ}

135^{\circ}=135^{\circ} \times \frac{\pi}{180} radian =\frac{3 \pi}{4} radian

Question 01(ix): 150^{\circ}

150^{\circ}=150^{\circ} \times \frac{\pi}{180} radian =\frac{5 \pi}{6} radian

Question 01(x): 10^{\circ}15^{\prime}

    \[\begin{aligned}  10^{\circ}15^{\prime}&=10^{\circ}\times \frac{15^{\circ}}{60}\\ & =10^{\circ}+\frac{1}{4} \\ & =\frac{40^{\circ}+1^{\circ}}{4}=\frac{41^{\circ}}{4} \\ & =\frac{41}{4} \times \frac{\pi}{180} \text { radian } \\ & =\frac{41 \pi}{720} \text { radian }\end{aligned}\]

Question 01(xi): 35^{\circ} 20^{\prime}

    \[\begin{aligned} 35^{\circ} 20^{\prime}&=35^{\circ}+\frac{20^{\circ}}{60}\\&=35^{\circ}+\frac{1^{\circ}}{3}\\ & =\frac{105^{\circ}+1^{\circ}}{3}\\&=\frac{106^{\circ}}{3} \\ & =\frac{106}{3} \times \frac{\pi}{180} \text { radian }\\&=\frac{53 \pi}{270} \text { radian } \end{aligned}\]

Question 01(xii): 75^{\circ} 6^{\prime} 30^{\prime \prime}

    \[\begin{aligned} $75^{\circ} 6^{\prime} 30^{\prime \prime} &=75^{\circ}+\frac{6^{\circ}}{60}+\frac{30^{\circ}}{3600}\\ & =75^{\mathrm{o}}+\frac{1^{\mathrm{o}}}{10}+\frac{1^{\mathrm{o}}}{120} \\ & =\left(75+\frac{1}{10}+\frac{1}{120}\right)^{\mathrm{o}} \\ & =\left(\frac{9000+12+1}{120}\right)^{\mathrm{o}} \\ & =\left(\frac{9013}{120}\right)^{\mathrm{o}} \\ & =\frac{9013}{120} \times \frac{\pi}{180} \text { radian }\\ &=\frac{9013 \pi}{21600} \text { radian } \end{aligned}\]

Question 01(xiii): 120^{\prime} 40^{\prime \prime}

    \[\begin{aligned} $120^{\prime} 40^{\prime \prime}&=\frac{120^{\circ}}{60}+\frac{40^{\circ}}{3600}\\ & =\left(\frac{120}{60}+\frac{40}{3600}\right)^{0} \\ & =\left(2+\frac{1}{90}\right)^{0}\\ &=\left(\frac{180+1}{90}\right)^{0}\\ &=\frac{181^{\circ}}{90}\\ &=\frac{181}{90} \times \frac{\pi}{180}\,\ \text{radian}\\ &=\frac{181}{16200} \pi \,\ \text{radian} \end{aligned}\]

Question 01(xiv): 154^{\circ} 20^{\prime \prime}

    \[\begin{aligned} 154^{\circ} 20^{\prime \prime}&=154^{\circ}+\frac{20^{\circ}}{3600}\\ &=154^{\circ}+\frac{20^{\circ}}{3600}\\ &=\left(154+\frac{1}{180}\right)^{0}\\ &=\left(\frac{27720+1}{180}\right)^{0}\\ &=\frac{27721^{\circ}}{180}\\ &=\frac{27721}{180} \times \frac{\pi}{180}\text { radian }\\ &=\frac{27721}{32400} \text { radian } \end{aligned}\]

Question 01(xiv): 0^{\circ}

    \[\begin{aligned} 0^{\circ}&=0 \times \frac{\pi}{180} \text { radian }\\ &=0 \text { radian } \end{aligned}\]

Question 01(xiv): 3^{\prime \prime}

    \[\begin{aligned}  3^{\prime \prime}&=\frac{3^{0}}{3600}\\ & =\frac{1^{\circ}}{1200} \\ & =\frac{1}{1200} \times \frac{\pi}{180} \text { radian } \\ & =\frac{\pi}{216000} \text { radian } \end{aligned}\]

Useful Links

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Apkplot.com is an all-in-one educational site that has answers to math problems and free past papers and MCQs to help people prepare for the MDCAT and ECAT. The website is based on FSC and covers the subjects of math, physics, chemistry, and biology for Parts 01 and 02. Students can use the website's large database of answers to math problems and step-by-step explanations to help them. Students taking FSC Parts 01 and 02, as well as the MCAT and ECAT, can also find past papers on the website. These papers help students understand the format of the exam and prepare well for the real test. The MCQs are also a great way for students to test their knowledge and figure out what they need to learn more about.
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