Question

Use the definition or identities to find the exact value of each of the remaining five trigonometric functions of the acute angle csc0 13 (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) cose- (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression) tan θ = (Simplifty your answer, including any radicals. Use integers or fractions for any numbers in the-expression.) sece- Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) coto- (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) Enter your answer in each of the answer boxes. Welrome to MuMathLah ere to search DOLL

Answer 1

Answer 2

SOLUTION :

Using t for theta for ease of typing.

So, 

sin t 

= 1/csc t 

= 1/13 (ANSWER)

cos t  

= sqrt(1 - sin^2 t)

= sqrt( 1 - (1/13)^2)

= sqrt(168)/13

= 2 sqrt(42) / 13 (ANSWER).

tan t 

= sin t / cost 

= (1/13) / (2 sqrt(42) / 13

= 1 / (2 sqrt(42))

= 1/2 sqrt(42) / 42

= 1/84 sqrt(42) (ANSWER).

sec t 

= 1/cos t 

= 1/(2 sqrt(42) / 13)

= 13/(2 sqrt(42))

= 13/2 sqrt(42) / 42

= 13/84 sqrt(42) (ANSWER).

cot t 

= 1/tan t

= 1/(1/84 sqrt(42))

= 84 sqrt(42)/42

= 2 sqrt(42) (ANSWER).