Question

If θ is acute and cos θ = 0.7258, find the value of 2 tan θ – sin θ.

Answer 1

Given: θ is acute and cos θ = 0.7258. Since θ is acute, sin θ > 0.

Step-wise calculation:

1. Compute cos² θ:

cos² θ = (0.7258)² 

= 0.52678564

2. Compute sin θ using sin² θ = 1 – cos² θ: 

`sin θ = sqrt(1 - 0.52678564)`

= `sqrt(0.47321436)`

= 0.68790578

3. Compute `tan θ = sin θ/cos θ`: 

`tan θ = 0.68790578/0.7258`

= 0.94778972

4. Compute 2 tan θ – sin θ:

2 tan θ – sin θ = 2(0.94778972) – 0.68790578

= 1.89557944 – 0.68790578

= 1.20767366

2 tan θ – sin θ = 1.207674, rounded to six decimal places.