Find the values of the six trigonometric functions of an angle in standard position where the terminal side is going through the point (-1, 1).
Sinθ =
Cosθ=
Tanθ=
Cscθ=
Secθ=
Cotθ=
it's clear you are in QII, since y>0 and x<0.
So, draw your triangle. The hypotenuse is √2, so now you can fill in the table.
Good
To find the values of the six trigonometric functions (sin, cos, tan, csc, sec, cot) of an angle in standard position where the terminal side is going through the point (-1, 1), we can use the following steps:
Step 1: Determine the values of the opposite side, adjacent side, and hypotenuse using the coordinates of the given point (-1, 1).
In this case, the point (-1, 1) represents the coordinates (x, y) = (-1, 1). The opposite side would be y = 1, the adjacent side would be x = -1, and the hypotenuse can be found using the Pythagorean theorem.
Step 2: Calculate the values of the six trigonometric functions.
1. Sinθ = opposite/hypotenuse
Plugging in the values we determined in step 1, sinθ = 1/hypotenuse. To find the hypotenuse, we can use the Pythagorean theorem: hypotenuse = √(opposite^2 + adjacent^2).
In this case, hypotenuse = √(1^2 + (-1)^2) = √(1 + 1) = √2.
Therefore, sinθ = 1/√2 = √2/2.
2. Cosθ = adjacent/hypotenuse
Using the values from step 1, cosθ = x/hypotenuse = -1/√2 = -√2/2.
3. Tanθ = opposite/adjacent
Therefore, tanθ = y/x = 1/-1 = -1.
4. Cscθ = 1/sinθ
Since we already found sinθ in step 2, cscθ = 1/(√2/2) = √2.
5. Secθ = 1/cosθ
Similarly, secθ = 1/(-√2/2) = -√2.
6. Cotθ = 1/tanθ
Also, cotθ = 1/(-1) = -1.
So, the values of the six trigonometric functions for the angle whose terminal side passes through the point (-1, 1) are:
Sinθ = √2/2
Cosθ = -√2/2
Tanθ = -1
Cscθ = √2
Secθ = -√2
Cotθ = -1.