Trigonometric identities and equations

Use the fundamental trigonometric identity:

sin² α + cos² α = 1.

1. Move sin² α to the other side: cos² α = 1 − sin² α.
2. Take the square root: cos α = √(1 − sin² α).
3. Because α is acute, its cosine is positive, so use the positive square root.
4. Round the result in the same way as the answer choices.

Use the fundamental trigonometric identity:

sin² α + cos² α = 1.

1. Move sin² α to the other side: cos² α = 1 − sin² α.
2. Take the square root: cos α = √(1 − sin² α).
3. Because α is acute, its cosine is positive, so use the positive square root.
4. Round the result in the same way as the answer choices.

The tangent function has a period of 180°, so its value repeats after every half-turn.

1. Treat the given angle as one solution of the equation.
2. Add any integer multiple of 180° to it.
3. Use k to represent any integer.

General solution: x = α + 180°k, where k ∈ ℤ and α is the angle given in the question.