Question

if sinO=-1÷2 and π<theta<3π÷2,find the value of cosO+tanO÷cotO+secO​

Answer 1

Answer: If sin θ = -1 / 2 and π < θ < 3π / 2, the values of cos θ and tan θ are cos θ = - √3 / 2 and tan θ = 1 / √3 respectively.

Let us see how we will use the concepts of trigonometry to find the values of cos θ and tan θ.

Explanation:

We have been given as sin θ = -1 / 2 . Using this we will calculate the value of θ .

Since, sin θ = -1 / 2 

θ = - π / 6 or 7π / 6 [Using trigonometric table of standard angle values]

But the range of θ is given as π < θ < 3π / 2

Therefore, we will consider θ = 7π / 6

Now, cos ( 7π / 6 ) = cos ( π + π / 6 ) = - cos ( π / 6 ) = - √3 / 2 .

Similarly, tan ( 7π / 6 ) = tan ( π + π / 6 ) = tan ( π / 6 ) = 1 / √3

Hence , cos θ = - √3 / 2 and tan θ = 1 / √3 .

Answer 2

We have been given as sin θ = -1 / 2 . Using this we will calculate the value of θ .

Since, sin θ = -1 / 2

θ = - π / 6 or 7π / 6 [Using trigonometric table of standard angle values]

But the range of θ is given as π < θ < 3π / 2

Therefore, we will consider θ = 7π / 6

Now, cos ( 7π / 6 ) = cos ( π + π / 6 ) = - cos ( π / 6 ) = - √3 / 2 .

Similarly, tan ( 7π / 6 ) = tan ( π + π / 6 ) = tan ( π / 6 ) = 1 / √3

Hence , cos θ = - √3 / 2 and tan θ = 1 / √3 .