Question

Use identities to find the exact values at α for the remaining five trigonometric functions. cosu--T and α is in quadrant lll. sín α Simplify your answer, including any radicals Use integers or fractions for any numbers in the expression) Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) seca Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) tan a Simplity your answer, including any radicals Use integers or fractions for any numbers in the expression) cot a Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Answer 1

cos α -- Since α is in quadrant III, only tan α and cota is positive 262 csc α = = sin α 62 cos α 62 sin α tan α- --or x31 cosa , tan α

Answer 2

SOLUTION :

Using a for alpha for ease of typing.

So, 

sin a

= sqrt( 1 - coś^2 a)

= sqrt( 1 - (-sqrt(2)/8)^2)

= sqrt( 1 - 2/64)

= sqrt(62/64)

=  +/- sqrt(62)/8 

= - sqrt(62) / 8 (ANSWER) (sin a is negative, since a is in quadrant III)

csc a 

= 1/sin a

= 1 / ( - sqrt(62)/8)

= - 8 / sqrt(62)

= - 8/62 sqrt(62)

= - 4/31 sqrt(62) (ANSWER).

sec a 

= 1/cos a

= 1/(- sqrt(2) / 8)

= - 8 / sqrt (2)

= - 8 sqrt(2) / 2

= - 4 sqrt(2) (ANSWER).

tan a 

= sin a / cos a 

= (- sqrt(62) / 8) / ( - sqrt(2) / 8)

= sqrt(62) / sqrt(2)

= sqrt (31) (ANSWER).

cot t 

= 1/tan a

= 1/(sqrt(31)

= 1/31 sqrt(31) (ANSWER).