The six trigonometric functions are:
1. sinθ = ₋2/√29
2. cosθ = ₋5/√29
3. tanθ = 2/5
4. cotθ = 5/2
5. secθ = ₋√29/5
6. cosecθ = ₋√29/2
Given, the point is (-5 , -2).
The angle is in the 3rd quadrant.
Find the length of the hypotenuse by using the Pythagorean Theorem.
c² = a² + b²
the length of side (a) = -5
the length of side (b) = -2
therefore, c² = (⁻5)² + (₋2)²
c² = 25 + 4
c² = 29
c = √29
c = 5.39
Now, values for the six trigonometric functions are:
sinθ = perpendicular/ base = b/c = ₋2/√29
cosθ = Adjacent/hypotenuse = a/c = ₋5/√29
tanθ = perpendicular/ adjacent = b/a = ₋2/₋5 = 2/5
cosecθ = 1/sinθ = 1/₋2/√29 = ₋√29/2
secθ = 1/cosθ = 1/₋5/√29 = ₋√29/5
cotθ = 1/tanθ = 1/2/5 = 5/2
hence we get the values of all the six trigonometric functions.
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