Question

Q1)find the values of the other five trigonometric functions using the given information 1) sin0 = 1/2, and 0 is in Quadrant II. 2)Cos0=-√2/2 , and 0 is in Quadrant III. 3) sec0 = 2√3/3 and 3π/2 < 0 < 2π.

4) tan0 = 1, and sin0 > O.

Answer 1

The values of the other five trigonometric functions for the given information are:

• sine (sin0) = 1/2, cosine (cos0) = -√3/2, tangent (tan0) = -√3/3, cosecant (csc0) = 2, secant (sec0) = -2√3/3, cotangent (cot0) = -√3 (for Quadrant II)
• sine (sin0) = -√2/2, cosine (cos0) = -√2/2, tangent (tan0) = 1, cosecant (csc0) = -√2, secant (sec0) = -√2, cotangent (cot0) = 1 (for Quadrant III)
• sine (sin0) = 1/2, cosine (cos0) = √3/2, tangent (tan0) = √3/3, cosecant (csc0) = 2, secant (sec0) = 2/√3, cotangent (cot0) = √3 (for 3π/2 < 0 < 2π)
• sine (sin0) = √2/2, cosine (cos0) = 1/2, tangent (tan0) = 1, cosecant (csc0) = √2, secant (sec0) = 2, cotangent (cot0) = 1 (for sin0 > 0)

Step-by-step explanation:

To find the values of the other five trigonometric functions, let's analyze each given information:

1. sin0 = 1/2, and 0 is in Quadrant II:In Quadrant II, the sine function is positive, the cosine function is negative, and the tangent function is positive. Since sin0 = 1/2, we can use the Pythagorean identity to find the value of cos0:cos^2(0) = 1 - sin^2(0)