Exam 6: Trigonometric Identities, Inverses, and Equations

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

Use a half-angle identity to rewrite the expression as a single, non-radical function.

Rewrite in terms of an expression containing only cosines to the power 1. sin² x cos⁴ x

Evaluate without using a calculator. Answer in radians.

Simplify without using a calculator.

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

Verify the equation is an identity by using fundamental identities and to combine terms.

Verify that the equation is an identity.

Find all real solutions. Answer in the exact form. Note that identities are not required to solve this exercise.

Use the following to answer questions : The volume of a cone is given by the formula where r is the radius, h is the height of the cone, and $\theta$ is the indicated complement of the angle of deflection $\alpha$ . Note that when , the formula becomes that of a right circular cone (if , then h is called the slant height or lateral height of the cone). -What angle $\theta$ was used if the radius is 8 ft, the slant height is 2 ft, and the volume of the cone is 104 ft³?

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

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

Solve using an identity. State all real solutions in radians rounded to four decimal places.

Use a cofunction identity to write an equivalent expression. cos 13°

Use the following to answer questions : The volume of a cone is given by the formula where r is the radius, h is the height of the cone, and $\theta$ is the indicated complement of the angle of deflection $\alpha$ . Note that when , the formula becomes that of a right circular cone (if , then h is called the slant height or lateral height of the cone). -Find the volume of a cone with radius 8 ft, slant height 4 ft, and angle of deflection $\alpha$ = 15°. Round to four decimal places.

Verify the equation is an identity using factoring and fundamental identities.

Find the exact value. sin 190° cos 55° - cos 190° sin 55°

Solve the equation in [0, 2π) using factoring by grouping. 4 tan² x cos² x - 12 cos² x + 3 = tan² x

Solve by factoring. State all real solutions in radians using the exact form. 2 cos² x + 11 cos x = 6

Solve using an identity. State all real solutions in radians using the exact form.