Question

If tan theta =(√2)/3, what is the value of cos theta?​

Answer 1

cos∅ = 3/√11

Explanation:

If tan ∅ = √(2)/3

We know the relationship:

• 1 + tan²∅ = sec²∅

As given, putting the value to this equation we get:

• 1 + (√(2)/3)² = sec²∅
• 1 + 2/9 = sec²∅
• 11/9 = sec²∅
• sec∅ = √(11)/3(Taking square root on both sides)

We know that sec∅ = 1/cos∅

Hence cos ∅ = 1/ sec∅

Putting the value of sec∅, we get:

• cos∅ = 1/(√11)/3
• cos∅ = 3/√11

This is an interesting method by using square relationship!

Answer 2

Answer: cos∅ = (3√11)/11

Explanation:

See image