Question

If sin(x) = 1/3 and sec(y) = 13/12 , where x and y lie between 0 and π/2, evaluate the expression using trigonometric identities. (Enter an exact answer.) cos(2y)

Answer 1

The expression using trigonometric identities = cos 2y = 2cos²A-1

y = 22.62° (quadrant 1)

Further explanation

Trigonometry is the science of mathematics that studies the relationship between sides and angles in triangles

Trigonometric identity is a sentence that contains trigonometric functions. The truth of this sentence is an identity that needs to be proven

There are several kinds of identity formulas that can be used

Double angle is multiplication of angles with integers

The value of the dual angle function can be derived from the trigonometric function of an angle. The relationship between the two can be obtained from the sum of the angles

Trigonometry Formulas for Double Angles:

sin 2A = 2 sin A cos A

cos 2A = 1 - 2 sin²A = 2cos²A-1

tan 2A = 2 tan A / 1-tan²A

In the task it is known that the value of sec (y) = 13/12, because

$sec (y) = \frac{1}{cos\:y}$

then $cos\:y=\frac{12}{13}$

so

$cos\:2y\:=\:2(\frac{12}{13})^2 - 1$

$cos\:2y=\:\frac{119}{169}$

cos 2y = 0.704

2y = 45.239°

y = 22.62° ( y lie between 0 and π/2)

Learn more

trigonometric ratio

brainly.com/question/9880052

Prove the converse of the Pythagorean Theorem

brainly.com/question/1597216

Use Pythagoras' theorem

brainly.com/question/10488367

the triangle angle

brainly.com/question/1611320

Keywords: trigonometric identities, sin, cos