inverse Trigonometric Functions Example 04.

Question:

Find the value of ( \theta ) in degrees, given that ( \sin(\theta) = 0.6 ).

Solution:

Start with the equation ( \sin(\theta) = 0.6 ).

Take the inverse sine (also known as arcsine) of both sides to solve for ( \theta ):

[ \theta = \sin^{-1}(0.6) ]

Use a calculator to find the value of ( \sin^{-1}(0.6) ). Round your answer to the nearest degree.

Substitute the value of ( \theta ) back into the original equation to verify your solution:

[ \sin(\theta) = \sin(\sin^{-1}(0.6)) ]

[ \sin(\theta) = 0.6 ]

Write the final answer as ( \theta = ) [value you calculated in step 3] degrees.