Question

If sinθ=106​, where θ is less than or equal to 90°, find the value of: a) sinθ+cosθ b) tanθ+1

Answer 1

The values of sinθ+cosθ and tanθ+1 can be found by using the Pythagorean identity and the definition of the tangent function, given that sinθ=1/6 and θ is in the first quadrant.

Step-by-step explanation:

Given that sinθ=1/6 and knowing that θ is less than or equal to 90°, we can find a) sinθ+cosθ and b) tanθ+1 by using the Pythagorean identity sin²θ + cos²θ = 1 and the definition of tanθ = sinθ/cosθ.

For a), sinθ+cosθ:

• First, find cosθ using the Pythagorean identity: cosθ = √(1 - sin²θ).
• Calculate cosθ = √(1 - (1/6)²).
• Sum sinθ and cosθ to find the value.

For b), tanθ+1:

• Use the value of cosθ found previously.
• Calculate tanθ as sinθ/cosθ.
• Add 1 to tanθ to get the result.