Evaluate a trigonometric ratio, and find an angle from its value

If sin θ = 0.5 for an acute angle, what does the inverse sine key return?

Could sin θ = 0.5 and cos θ = 0.5 give different acute angles?

Compare the table at 30°, 45° and 60°. Locate 0.5 in the sine or cosine row and compare the tangent values

Which inverse matches tangent equal to one?

Recover the angle

Match the inverse key to the stated ratio and set degree mode. Acute sine and cosine are between zero and one; tangent is positive and may exceed one

1. 1Inverse is not reciprocal The superscript −1 names the inverse function here. It does not mean one divided by the function
2. 2Use all given digits If a ratio value is given, use that value as stated. If lengths are given, enter their original quotient rather than rounding it first
3. 3Check a known value Inverse sine of 0.5 should report 30° in degree mode \(\displaystyle \sin^{-1}(0.5)=30^{\circ}\)

Given

\(\displaystyle \sin θ=0.64\)

An acute angle has sine 0.64. Find the angle to one decimal place

Given

\(\displaystyle \cos θ=0.64\)

An acute angle has cosine 0.64. Find the angle to one decimal place

Given

\(\displaystyle \tan θ=1.6\)

An acute angle has tangent 1.6. Find the angle to one decimal place

A calculator gives a domain error for sin⁻¹(1.6). What is the correct interpretation?

Inverse sine of 0.5 displays about 0.524. What should you change to obtain degrees?