Home fsc 1st year math solutions Trigonometric Ratios of Allied Angles Exercise 10.1

Trigonometric Ratios of Allied Angles Exercise 10.1

Trigonometric Identities 10.1
Trigonometric Identities 10.1
  1. Without using the tables, find the values of:
    i) \sin \left(-780^{\circ}\right)
    ii) \cot \left(-855^{\circ}\right)
    iii) \csc \left(2040^{\circ}\right)
    iv) \sec \left(-960^{\prime}\right)
    v) \tan \left(1110^{\circ}\right)
    vi) \sin (-300)
  2. Express each of the following as a trigonometric function of an angle of positive degre measure of less than 45^{\circ}.
    i) \sin 196^{\circ}
    ii) \cos 147^{\circ}
    iii) \sin 319^{\prime}
    iv) \cos 254
    v) \tan 294
    vi) \cos 728
    vii) \sin \left(-625^{\circ}\right) \quad viii) \cos \left(-435^{\circ}\right) \quad ix) \sin 150^{\circ}
  3. Prove the following:
    i) \sin \left(180^{\circ}+\alpha\right) \sin (90-\alpha)=\sin \alpha \cos \alpha
    ii) \sin 780^{\circ} \sin 480^{\circ}+\cos 120^{\circ} \sin 30^{\circ}=\frac{1}{2}
    iii) \cos 306^{\prime}+\cos 234^{\prime}+\cos 162^{\prime}+\cos 18^{\prime}=0
    Iv) \cos 330^{\circ} \sin 600^{\circ}+\cos 120^{\circ} \sin 150^{\circ}=1
  1. Prove that:
    i) \sin ^2(\pi+\theta) \tan \left(\frac{3 \pi}{2}+\theta\right) \frac{2}{\cot ^2\left(\frac{3 \pi}{2}-\theta\right) \cos ^2(\pi-\theta) \operatorname{coses}(2 \pi-\theta)}=\cos \theta
    ii) \frac{\cos \left(90^{\circ}+\theta\right) \sec (-\theta) \tan \left(180^{\circ}-\theta\right)}{\sec \left(360^{\circ}-\theta\right) \sin \left(180^{\circ}+\theta\right) \cot \left(90^{\circ}-\theta\right)}=-1
  2. If \alpha, \beta, \gamma are the angles of a triangle \mathrm{ABC}, then prove that
    i) \sin (\alpha+\beta)=\sin \gamma
    ii) \cos \left(\frac{\alpha+\beta}{2}\right)=\sin \frac{\gamma}{2}
    iii) \cos (\alpha+\beta)=\cos \gamma
    Iv) \tan (\alpha+\beta)+\tan \gamma=0
Previous articleApplications of basic Identities Exercise 10.2
Next articleSum, Difference and Product of Sines and Cosines Exercise 10.4
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.



Please enter your comment!
Please enter your name here

We use cookies to ensure that we give you the best experience on our website.