Find the values of other five trigonometric functions if tan x = -5/12, and x lies in the second quadrant.
Question
Find the values of other five trigonometric functions if , and lies in the second quadrant.
Solution
Sure, let's solve this step by step.
Step 1: We know that tan x = -5/12. The negative sign indicates that x is in the second quadrant where tan is negative.
Step 2: We also know that tan x = sin x / cos x. So, we can say that sin x = -5 and cos x = 12 (considering a right triangle where the opposite side is -5 and the adjacent side is 12).
Step 3: To find the hypotenuse (r) of this right triangle, we can use the Pythagorean theorem: r = sqrt((-5)^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13.
Step 4: Now, we can find the values of the other trigonometric functions:
- sin x = -5/13 (opposite/hypotenuse)
- cos x = 12/13 (adjacent/hypotenuse)
- csc x = 1/sin x = -13/5
- sec x = 1/cos x = 13/12
- cot x = 1/tan x = -12/5
So, the values of the six trigonometric functions are: sin x = -5/13, cos x = 12/13, tan x = -5/12, csc x = -13/5, sec x = 13/12, and cot x = -12/5.
Similar Questions
Find sin(2x), cos(2x), and tan(2x) from the given information.tan(x) = − 125, x in Quadrant II
Find the values of other five trigonometric functions if cot x = 3/4, x lies in the third quadrant.
Find sen2x, cos2x, and tan2x if =senx−1213 and x terminates in quadrant IV.sen2x = cos2x = tan2x =
Find the values of the trigonometric functions of t from the given information.csc(t) = 6, cos(t) < 0sin(t) = cos(t) = tan(t) = sec(t) = cot(t) =
Use the sum and difference identities to determine the exact value of the following expression.sin(5π12)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.