Exam 6: Trigonometric Identities, Inverses, and Equations

Find the exact value.

Use a cofunction identity to write an equivalent expression.

Find exact values for ;

Rewrite as a single expression. sin(6 $\theta$ )cos(3 $\theta$ ) - cos(6 $\theta$ )sin(3 $\theta$ )

State the period P of the function and find all solutions in [0, P).

Evaluate without the aid of calculators or tables. Answer in radians.

Evaluate without the aid of calculators or tables, keeping the domain and range of the function in mind. Answer in radians.

Verify the equation is an identity using multiplication and fundamental identities. cos x (sec x - cos x) =

Starting with the ratio identity given, use substitution and fundamental identities to write a new identity belonging to the ratio family.

Evaluate using a calculator. Answer to the nearest tenth of a degree. sec^-1 5.593

Verify that the equation is an identity.

Rewrite as a single expression. cos(10 $\theta$ )cos(6 $\theta$ ) - sin(10 $\theta$ )sin(6 $\theta$ )

Rewrite the product as a sum using a product-to-sum identity. 2sin(2073\9\pi\)t)cos(813 $\pi$ t)

Use the following to answer questions : $\alpha$ and $\beta$ are acute angles with tan( $\alpha$ ) = and sec( $\beta$ ) = . -Find tan( $\alpha$ - $\beta$ ).

Use the following to answer questions : $\alpha$ and $\beta$ are acute angles with tan( $\alpha$ ) = and sec( $\beta$ ) = . -Find cos( $\alpha$ + $\beta$ ).

Write cot x entirely in terms of cos x.

Use the following to answer questions : $\alpha$ and $\beta$ are acute angles with tan( $\alpha$ ) = and sec( $\beta$ ) = . -Find sin( $\alpha$ + $\beta$ ).

Solve the equation in [0, 2π) by squaring both sides. sec x - tan x = -1

Evaluate using a calculator. Answer in radians to the nearest ten-thousandth, in degrees to the nearest tenth.

Use the following to answer questions : The graph of y = csc(x) is shown below. Draw the horizontal line y = -1.5. -State the quadrant of the principal root.