Respuesta :
Answer:
the reference angle is given by [tex]\frac{\pi}{3}[/tex]
sine = negative
cosine = positive
tangent = negative
Step-by-step explanation:
We have been given the angle [tex]\theta=\frac{5\pi}{3}[/tex]
The angle lies in Quadrant IV. Hence, in order to find the reference angle, we can subtract this angle with [tex]2\pi[/tex]
Therefore, the reference angle is given by
[tex]2\pi - \frac{5\pi}{3} \\\\=\frac{\pi}{3}[/tex]
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:
The reference angle is [tex]\frac{\pi}{3}[/tex]. Sine:negative, Cosine:positive, Tangent:Negative
Step-by-step explanation:
Given an angle that is in the range [tex][0,2\pi][/tex], 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 [tex]180-\theta[/tex]
3. If the angle is in the third quadrant, then the reference angle is [tex]\theta-180[/tex]
4. If the angle is in the fourth quadrant, then the reference angle is [tex]360-\theta[/tex]
We are given that [tex]\theta = \frac{5 \pi}{3}[/tex]. This angle is in the range [tex][0,2\pi][/tex], and this angle is in the fourth quadrant. Recall that 360° are equivalent to[tex] 2\pi[/tex] radians.
So the reference angle is
[tex] 2\pi - \frac{5\pi}{3} = \frac{\pi}{3}[/tex].
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.
