Question

Suppose
cos(π/2−x) =3/5, cos x =4/5
find sin, tan, csc, sec, cot

Answer 1

To find the values of sin, tan, csc, sec, and cot, we use trigonometric identities and given information. Sin x = 3/5, tan x = 3/4, csc x = 5/3, sec x = 5/4, and cot x = 4/3.

Step-by-step explanation:

To find the values of sin, tan, csc, sec, and cot, we can use the trigonometric identities. From the given information, we know that cos x = 4/5. Using the Pythagorean identity, sin² x = 1 - cos² x, we can find sin x as:

sin x = sqrt(1 - (4/5)²) = sqrt(1 - 16/25) = sqrt(9/25) = 3/5

Now, we can calculate the remaining trigonometric values:

tan x = sin x / cos x = (3/5) / (4/5) = 3/4

csc x = 1 / sin x = 1 / (3/5) = 5/3

sec x = 1 / cos x = 1 / (4/5) = 5/4

cot x = 1 / tan x = 1 / (3/4) = 4/3

Answer 2

cos (π/2 - x) = sin x = 3/5
tan x = sin x / cos x = 3/5 / 4/5 = 3/4
csc x = 1/sin x = 1 / 3/5 = 5/3
sec x = 1/cos x = 1 / 4/5 = 5/4
cot x = 1/tan x = 1 / 3/4 = 4/3.