Determine the exact values of the trigonometric functions of the acute angle A,
given tan A =3/7 ?

Question

Grace Ashcraft · Accepted Answer

see explanation

Tan A = 3/7 specifies a right triangle with base = 7, height = 3. (because by definition Tan A = height/base). The hypotenuse of the triangle is then #sqrt(7^2 + 3^2) = 7.616# (rounding). And with this information, you can calculate the other trig values for the triangle: #sin a = 3/7.616# #cos a = 7/7.616# ...and, as a final sanity check, you can use the alternate definition for Tan A: #tan a = (sin a)/(cos a)# # = (3/7.616)/(7/7.616)# # = 3/7.616 * 7.616/7# # = 3/7# ...which checks out. I won't calculate sec a, csc a, cot a for you, you should be able to take it from here, since: #sec a = 1/(cos a)#, #csc a = 1/(sin a)#, and #cot a = 1/(tan a)# GOOD LUCK

Abigail Armstrong · Answer

#sin(A) = (3sqrt58)/58#
#csc(A) = sqrt58/3#
#cos(A) = (7sqrt58)/58#
#sec(A) = sqrt58/7#
#cot(A) = 7/3# Given: #tan(A) = 3/7, 0< A < pi/2# Use the identity #cot(A) = 1/tan(A)# #cot(A) = 7/3# Use the identity #1+tan^2(A)=sec^2(A)# #1 + (3/7)^2= sec^2(A)# #1 + 9/49= sec^2(A)# #sec^2(A) = 58/49# #sec(A) = sqrt58/7# Using the identity #cos(A) = 1/sec(A)# #cos(A) = (7sqrt58)/58# Using the identity #tan(A) = sin(A)/cos(A)# #3/7 = sin(A)/((7sqrt58)/58)# #sin(A) = (3sqrt58)/58# Use the identity #csc(A) = 1/sin(A)# #csc(A) = sqrt58/3#

Determine the exact values of the trigonometric functions of the acute angle A, given tan A =3/7 ?