Question

When ø=5pi/3, what are the reference angle and the sign values for sine, cosine, and tangent? (2

Answer 1

Answer:

the reference angle is given by $\frac{\pi}{3}$

sine = negative

cosine = positive

tangent = negative

Step-by-step explanation:

We have been given the angle $\theta=\frac{5\pi}{3}$

The angle lies in Quadrant IV. Hence, in order to find the reference angle, we can subtract this angle with $2\pi$

Therefore, the reference angle is given by

$2\pi - \frac{5\pi}{3} \\\\=\frac{\pi}{3}$

In Quadrant IV, cosine and secant functions are positive and rest trigonometric functions are negative.

Thus, we have

sine = negative

cosine = positive

tangent = negative

Answer 2

Answer:

The reference angle is $\frac{\pi}{3}$. Sine:negative, Cosine:positive, Tangent:Negative

Step-by-step explanation:

Given an angle that is in the range $[0,2\pi]$, you must apply the following:

1. If the angle is in the first quadrant, then the reference angle is the same.

2. If the angle is in the second quadrant, then the reference angle is $180-\theta$

3. If the angle is in the third quadrant, then the reference angle is $\theta-180$

4. If the angle is in the fourth quadrant, then the reference angle is $360-\theta$

We are given that $\theta = \frac{5 \pi}{3}$. This angle is in the range $[0,2\pi]$, and this angle is in the fourth quadrant. Recall that 360° are equivalent to$2\pi$ radians.

So the reference angle is

$2\pi - \frac{5\pi}{3} = \frac{\pi}{3}$.

The sign of the sine of this angle is determined of the sign of the y coordinate of one number of the same quadrant. Take for example the number (1,-1). This means that sine has a negative sign. To check the cosine sign, we check the sign of the x coordinate of (1,-1). Since it is positive, the cosine is positive.

Since tangent = sine/cosine and taking into account the law of signs, we have that tangent has a negative sign in this quadrant.