Question

If sinθ = 12/13. Find the value of sin³θ + cos³θ, where θ lies in postive quadrant. 
1. 1653/2197
2. 1753/2197
3. 1853/2197
4. 1453/2197

Answer 1

Correct Answer - Option 3 : 1853/2197

Given:

sinθ = 12/13

Concept used:

If θ is in the positive quadrant then the value of all trigonometric ratios will be a positive value.

Formula used:

sinθ = perpendicular/hypotenuse

cosθ = base/hypotenuse

According to pythagoras theorem,

hypotenuse² = perpendicular² + base² 

Calculation:

sinθ = 12/13 = perpendicular/hypotenuse

Here, perpendicular = 12

And hypotenuse = 13

Then, base2 = 132 - 122

⇒ base2 = 169 - 144

⇒ base2 = 25

⇒ base = √25

⇒ base = 5

Now, sin3θ + cos3θ = (12/13)³ + (5/13)³

⇒ (1728/2197) + (125/2197)

⇒ 1853/2197

∴ The value of sin3θ + cos3θ is 1853/2197.