1. Use the identity $\sin^2(\theta) + \cos^2(\theta) = 1$. 2. Solve for sin(θ). 3. Determine the sign of sin(θ) based on the given quadrant.

1. Find the principal angle θ in the range [-π/2, π/2]. 2. Find the other angle in [0, 2π] using symmetry. 3. Add 2πk to each to find all coterminal angles.

1. If sin(θ) > 0 and cos(θ) > 0, the angle is in Quadrant I. 2. If sin(θ) > 0 and cos(θ) < 0, the angle is in Quadrant II. 3. If sin(θ) < 0 and cos(θ) < 0, the angle is in Quadrant III. 4. If sin(θ) < 0 and cos(θ) > 0, the angle is in Quadrant IV.

1. If angle is in QI, reference angle = angle. 2. If angle is in QII, reference angle = 180 - angle (in degrees) or π - angle (in radians). 3. If angle is in QIII, reference angle = angle - 180 (in degrees) or angle - π (in radians). 4. If angle is in QIV, reference angle = 360 - angle (in degrees) or 2π - angle (in radians).

1. Recall tan(θ) = sin(θ)/cos(θ). 2. Find angles where sin(θ) and cos(θ) are equal. 3. Identify θ = π/4 and θ = 5π/4 as solutions in [0, 2π).

1. Recognize that sine is an odd function, so sin(-θ) = -sin(θ). 2. Find the value of sin(θ). 3. Change the sign to find sin(-θ).

1. Recognize that cosine is an even function, so cos(-θ) = cos(θ). 2. Find the value of cos(θ). 3. The value is the same.

1. Recognize sin(θ) = 0.5 corresponds to π/6. 2. Identify the second quadrant angle where sin(θ) is also 0.5, which is 5π/6.

1. Identify the angle on the unit circle. 2. Determine the sine, cosine, and tangent values for that angle. 3. Substitute these values into the expression and simplify.

1. Recall cos(θ) represents the x-coordinate on the unit circle. 2. Identify the angle where the x-coordinate is -1. 3. θ = π.

A circle with a radius of 1, centered at the origin (0,0).

An angle that starts from the positive x-axis and goes counterclockwise.

A unit of angular measure equal to the angle subtended at the center of a circle by an arc equal in length to the radius.

A line from the origin at a given angle that intersects the unit circle.

The y-coordinate of the point where the terminal ray intersects the unit circle.

The x-coordinate of the point where the terminal ray intersects the unit circle.

The ratio of the y-coordinate to the x-coordinate (sin θ / cos θ) of the point where the terminal ray intersects the unit circle.

Angles greater than 180° but less than 360°.

2π radians.

A mnemonic to remember which trig functions are positive in each quadrant: All, Sine, Tangent, Cosine.

$\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$

$\pi \text{ radians} = 180^{\circ}$

$P = (\cos(\theta), \sin(\theta))$

$\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$

$\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$

$\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}$

$\text{radians} = \text{degrees} \times \frac{\pi}{180}$

$\text{degrees} = \text{radians} \times \frac{180}{\pi}$

$x^2 + y^2 = r^2$, and since r=1, $x^2 + y^2 = 1$

$\theta + 2\pi k$, where k is an integer.