Given sec A =13/6 and that angle A is in Quadrant I, find the exact value of sin A in simplest radical form using a rational denominator.

Answer 1

Given Sec A = 13/6 find exact value of Sin A in simplest radical form.

First, we know that Sec A = 1/Cos A

1/Cos A = 13/6

Multiply both sides by Cos A yields 1= (13/6) Cos A

Cos A = 6/13

Since we are in the first quadrant, Sin A also has to be positive.

A common identity is Cos² A + Sin² A = 1

Let's substitute: (6/13)² + Sin² A = 1

Let's isolate Sin² A: Sin² A = 1- (6/13)²

Simplify: Sin² A = 1- (36/169)

Sin² A = (169/169)-(36/169)

Sin² A = 133/169

Take Square Root of both sides:

Sin A = ((133)^1/2/13)

Answer 2

sinA = 2/√13

cosA = √(1 - sin²A) = √(1 - 4/13) = √(9/13) = 3/√13

tanA = sinA / cosA = (2/√13) / (3/√13) = 2/3

Answer 3

cos A = 1/sec A, so cos A = 1/(13/6) = 6/13

In Quadrant 1, sin A > 0.

Thus, as sin²A + cos²A = 1 for all A

sin A = √(1 - (6/13)²) =

√(1 - 36/169) =

√(133/169) =

√133 / 13

Answer 4

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