1. cos theta = 0.2 for 270 degrees <= theta <= 360 degrees.
Ans: 78.5 degs?
2. sin theta = 0.95 for -90 degrees <= theta <= 90 degrees.
Ans: 71.8 degs?
1.
78.5° would be the answer if the angle had been acute, but you wanted the angle in the 4th quadrant
so Ø = 360 - 78.463 = 281.5°
check by taking cos 281.5°
2.
Again you want -90 ≤ Ø ≤ 90, which would be quadrant I or quadrant IV
but for sinØ = .95, the sine is positive in the first quadrant and not in the IV
so you are correct
Again, you could have checked your answer by taking sin 71.8°
To find the angle theta given a trigonometric function value, you can use the inverse trigonometric functions.
1. To find theta when cos theta = 0.2 for 270 degrees <= theta <= 360 degrees:
Use the inverse cosine function (also known as arccos or cos^(-1)) to find the angle when the cosine value is given.
cos^(-1)(0.2) = 78.5 degrees
So theta is approximately 78.5 degrees.
2. To find theta when sin theta = 0.95 for -90 degrees <= theta <= 90 degrees:
Use the inverse sine function (also known as arcsin or sin^(-1)) to find the angle when the sine value is given.
sin^(-1)(0.95) = 71.8 degrees
So theta is approximately 71.8 degrees.
To find the value of theta when the cosine or sine is given, we need to use the inverse cosine (arccos) or inverse sine (arcsin) function. These functions give us the angle whose cosine or sine is equal to the given value.
1. For cos(theta) = 0.2, we need to find theta in the range 270 degrees <= theta <= 360 degrees.
Using the inverse cosine function, we can write this as:
theta = arccos(0.2)
To find the value of theta, we can use a calculator or a table of trigonometric functions. Evaluating arccos(0.2), we get:
theta ≈ 78.5 degrees
So the value of theta in the given range is approximately 78.5 degrees.
2. For sin(theta) = 0.95, we need to find theta in the range -90 degrees <= theta <= 90 degrees.
Using the inverse sine function, we can write this as:
theta = arcsin(0.95)
Again, we can use a calculator or a table of trigonometric functions to evaluate arcsin(0.95). We get:
theta ≈ 71.8 degrees
So the value of theta in the given range is approximately 71.8 degrees.