Question

Supposeθis an acute angle (so 0◦< θ <90◦) and sinθ= 1/4. Determine the exact values of theother 5 trigonometric functions ofθ. ?

Answer 1

`tan θ=1/sqrt(15)`

`cos θ=sqrt(15)/4`

`cosec θ=4`

`sec θ=4/sqrt(15)`

`cot θ=sqrt(15)`

Explanation:

`sin θ="opposite"/"hypotenuse" =(1/4)`
So, opposite =1 , hypotenuse = 4 , adjacent =`(sqrt(4^2-1^2))=(sqrt(15))`

`tan θ= "opposite"/"adjacent"`

`cos θ="adjacent"/"hypotenuse"`

`cosec θ=(1)/sinθ=(1)/("opposite"/"hypotenuse")="hypotenuse"/"opposite"`

`sec θ=1/cosθ=1/("adjacent"/"hypotenuse")="hypotenuse"/"adjacent"`

`cot θ=(1)/(tanθ)=(1)/("opposite"/"adjacent")="adjacent" /"opposite"`

Substitute the value of opposite , adjacent , and hypotenuse into the formulae , the you will get the answers.