Exam 6: Trigonometric Identities, Inverses, and Equations

Evaluate using a calculator, keeping the domain and range of the function in mind. Answer in radians to the nearest ten-thousandth and in degrees to the nearest tenth.

Rewrite the product as a sum using a product-to-sum identity. sin(-10 $\alpha$ )sin(4 $\alpha$ )

Use the following to answer questions : tan $\theta$ = ; $\theta$ in QII. -Find the exact value of sin(2 $\theta$ ).

Rewrite as a single expression. sin(7 $\theta$ )cos(3 $\theta$ ) + cos(7 $\theta$ )sin(3 $\theta$ )

Rewrite as a single expression.

Rewrite the sum as a product using a sum-to-product identity.

Find the exact value of the expression using a sum or difference identity. Some simplifications may involve using symmetry and the formula for negatives. cos 165°

Use a double-angle identity to find the exact value.

Evaluate without the aid of calculators or tables. Answer in radians. cos^-1 1

Verify the equation is an identity using special products and fundamental identities. (1 + cos x)[1 - cos(-x)] = sin² x

Find all solutions in [0, 2π). Answer in the exact form. 3.5 cos x + 5 = 3.25

Evaluate. Answer in exact form.

Use the following to answer questions : The graph of y = csc(x) is shown below. Draw the horizontal line y = -1.5. -State the number of roots in [0, 2 $\pi$ ].

Solve the equation in [0, 2π) using identities. cos(8x)cos(5x) + sin(8x)sin(5x) + cos(3x) + 1 = 0

The range of a projectile is modeled by the function , where v is the initial velocity and $\theta$ is the angle at which the object is initially propelled. The maximum range is achieved when $\theta$ = 45°. Use exact values to compute how many feet short of maximum the projectile falls if $\theta$ = 67.5° and v = 104 ft/sec.

Use a double-angle identity to find the exact value. cos 105° sin 105°

Evaluate. Answer in exact form.