Which of the following is equivalent to sec θ
A. 1/sin θ
B. 1/cos θ
C. 1/tan θ
D. sin θ / cos θ
Simplify the trigonometric expression: 1 + tan²θ
A. cosec²θ
B. sec²θ
C. cot²θ
D. sin²θ
What is the exact value of sin 30° cos 60° + cos 30° sin 60°?
A. 0
B. 1/2
C. 1
D. √3/2
Expand and simplify cos(x - 45°).
A. cos x cos 45° + sin x sin 45°
B. cos x cos 45° - sin x sin 45°
C. sin x cos 45° + cos x sin 45°
D. sin x cos 45° - cos x sin 45°
Given that sin x = 3/5 and x is an acute angle, find the exact value of cos 2x.
A. 7/25
B. 24/25
C. -7/25
D. -24/25
Find the exact value of tan 105°.
A. 2 + √3
B. 2 - √3
C. -2 - √3
D. -2 + √3
Solve the equation cot x = -1 for 0° ≤ x < 360°.
A. 45°, 225°
B. 135°, 315°
C. 45°, 135°, 225°, 315°
D. No solution
When 3 sin θ + 4 cos θ is expressed in the form R sin(θ + α), where R > 0 and 0° < α < 90°, what is the value of R?
3
4
5
7
The maximum value of the expression 12 cos θ - 5 sin θ is:
5
12
13
17
The minimum value of 10-12 cos θ + 5 sin θ=______.
Solve the equation sin 2θ = cos θ for 0° ≤ θ < 360°.
A. 30°, 90°, 150°, 270°
B. 0°, 90°, 180°, 270°
C. 0°, 30°, 150°, 180°
D. 30°, 60°, 150°, 270°
Solve the equation 3 sec²θ - 10 tan θ = 0 for 0° ≤ θ < 360°.
A. 18.4°, 71.6°
B. 18.4°, 198.4°
C. 71.6°, 251.6°
D. 18.4°, 71.6°, 198.4°, 251.6°
The equation 3 tan(x + 45°) = tan(x - 45°) can be written in the form a tan²x + b tan x + c = 0. Find the value of a + b + c.
0
1
2
3