Respuesta :
Answer:
e) [tex] \pi/2 [/tex]
f) [tex] 3\pi/2 [/tex]
g) [tex] 0 [/tex]
h) [tex] \pi [/tex]
i) [tex] \pi/4 [/tex]
j) [tex] 3\pi/4 [/tex]
Step-by-step explanation:
We can solve this exercise by watching a basic trigonometric table
Here i will list values of sin and cos in the points [tex] 0, \pi/4, \pi/2, 3\pi/4 [/tex] and [tex] \pi [/tex]
- [tex] cos(0) = 1 [/tex]
- [tex] sin(0) = 0 [/tex]
- [tex] cos(\pi/4) = \sqrt2 / 2 [/tex]
- [tex] sin(\pi/4) = \sqrt2 / 2 [/tex]
- [tex] cos(\pi/2) = 0 [/tex]
- [tex] sin(\pi/2) = 1 [/tex]
- [tex] cos(3 \pi/4) = -\sqrt2 / 2 [/tex]
- [tex] sin(3 \pi/4) = \sqrt2 / 2 [/tex]
- [tex] cos(\pi) = -1 [/tex]
- [tex] sin(\pi) = 0 [/tex]
Hence, the sin takes the value 1 on [tex] \pi/2 [/tex], while it takes the value -1 in its opposite value - \pi/2 (because it is an odd function). If we use the periodicity of the sin, then sin(- \pi/2 + 2 \pi) = -1. Hence [tex] sin^{-1}(-1) = 3 \pi/2 [/tex]
The cos takes value 1 in 0, and it takes the value -1 in [tex] \pi [/tex]
The tangent is the quotient between sin and cos. The tangent is 1 when both cos and sin are equal. We can see that they are equal in [tex] \pi/4 [/tex], where they take the value [tex] \sqrt2 / 2 [/tex]
The tangent is -1 where they are the opposite. This happens in [tex] 3 \pi/4 [/tex] where they take the value [tex] \sqrt 2/2 [/tex] and [tex] - \sqrt2 /2 [/tex] respectively.
