Question

In the following problems the values of sin(θ)and cos(θ)are given. Determine the value of tan(θ).

a. sin(θ)=0.1 and cos(θ)=0.995

tan(θ)=

b. sin(θ)=−0.158 and cos(θ)=−0.987

tan(θ)=

c. sin(θ)=−0.631and cos(θ)=0.776

tan(θ)=​

Answer 1

a) ≈ 0.1

b) ≈ 0.2

c) ≈ 0.9

Explanation:

GIVEN :-

• Values of sinθ & cosθ

TO FIND :-

• Value of tanθ

FACTS TO KNOW BEFORE SOLVING :-

• 
  `\tan \theta = (\sin \theta)/(\cos \theta)`

SOLUTION :-

a)
`\tan \theta = (\sin \theta)/(\cos \theta) = (0.1)/(0.995)` ≈ 0.1

b)
`\tan \theta = (\sin \theta)/(\cos \theta) = (-0.158)/(-0.987) = 0.16 (appx)` ≈ 0.2

c)
`\tan \theta = (\sin \theta)/(\cos \theta) = (0.631)/(0.776) = 0.81 (appx)` ≈ 0.9