Solve for \(\theta\) in the following equation: \(\sin 2\theta = \cos \theta\)
A\(30^\circ\)
B\(45^\circ\)
C\(60^\circ\)
D\(15^\circ\)
Mathematics · Question Bank
Trigonometry
85 questions · page 3 of 5. Answer in your head first, then check the solution.
If \(\sin 3A = \cos 6B\) then
A\(A+B=90^\circ\)
B\(A+2B=30^\circ\)
C\(A+B=180^\circ\)
DNone of these
Solve for x, if \(\tan 3x = 5 \tan x\).
A\(20.705^\circ\)
B\(30.705^\circ\)
C\(35.705^\circ\)
D\(15.705^\circ\)
If \(\sin x \cos x + \sin 2x = 1\), what are the values of x?
A\(32.2^\circ, 69.3^\circ\)
B\(-20.67^\circ, 69.3^\circ\)
C\(20.90^\circ, 69.1^\circ\)
D\(-32.2^\circ, 69.3^\circ\)
Solve for G if \(\csc(11G - 16^\circ) = \sec(5G + 26^\circ)\).
A\(7^\circ\)
B\(5^\circ\)
C\(6^\circ\)
D\(4^\circ\)
Find the value of A between \(270^\circ\) and \(360^\circ\) if \(2 \sin^2 A - \sin A = 1\)
A\(300^\circ\)
B\(320^\circ\)
C\(310^\circ\)
D\(330^\circ\)
If \(\cos 65^\circ + \cos 55^\circ = \cos \theta\), find \(\theta\) in radians.
A0.765
B0.087
C1.213
D1.421
Find the value of \(\sin(\text{arc} \cos \frac{15}{17})\).
A8/11
B8/19
C8/15
D8/17
The sine of a certain angle is 0.6, calculate the cotangent of the angle.
A4/3
B5/4
C4/5
D3/4
If \(\sec 2A = \frac{1}{\sin 13A}\), determine the angle A in degrees.
A\(5^\circ\)
B\(6^\circ\)
C\(3^\circ\)
D\(7^\circ\)
If \(\tan x = \frac{1}{2}\), \(\tan y = \frac{1}{3}\), what is the value of \(\tan(x+y)\)?
A1/2
B1/6
C2
D1
Find the value of y in the given: \(y = (1 + \cos 2\theta) \tan \theta\).
A\(\sin \theta\)
B\(\cos \theta\)
C\(\sin 2\theta\)
D\(\cos 2\theta\)
Find the value of \(\frac{\sin \theta + \cos \theta \tan \theta}{\cos \theta}\)
A\(2 \sin \theta\)
B\(2 \cos \theta\)
C\(2 \tan \theta\)
D\(2 \cot \theta\)
Simplify the equation \(\sin^2 \theta (1 + \cot^2 \theta)\)
A1
B\(\sin^2 \theta\)
C\(\sin^2 \theta \sec^2 \theta\)
D\(\sec^2 \theta\)
Simplify the expression \(\sec \theta - (\sec \theta)\sin^2 \theta\)
A\(\cos^2 \theta\)
B\(\cos \theta\)
C\(\sin^2 \theta\)
D\(\sin \theta\)
Arc tan \([2 \cos (\text{arc} \sin [(3^{1/2})/2])]\) is equal to
A\(\pi/3\)
B\(\pi/4\)
C\(\pi/16\)
D\(\pi/2\)
Evaluate arc cot \([2\cos (\text{arc} \sin 0.5)]\)
A\(30^\circ\)
B\(45^\circ\)
C\(60^\circ\)
D\(90^\circ\)
Solve for x in the given equation: Arc tan (2x) + arc tan (x) = \(\frac{\pi}{4}\)
A0.149
B0.281
C0.421
D0.316
Solve for x in the equation: arc tan (x + 1) + arc tan (x-1) = arc tan (12).
A1.5
B1.34
C1.20
D1.25
Solve for A for the given equation \(\cos^2 A = 1 - \cos^2 A\).
A45, 125, 225, 335 degrees
B45, 125, 225, 315 degrees
C45, 135, 225, 315 degrees
D45, 150, 220, 315 degrees