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)

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

then

so

cos 2y = 0.704

2y = 45.239°

y = 22.62° ( y lie between 0 and π/2)

Learn more

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Prove the converse of the Pythagorean Theorem

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Use Pythagoras' theorem

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the triangle angle

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Keywords: trigonometric identities, sin, cos

The least natural number is 103(there's probably a better way to do this, but this is what i have.)for dividing by 24: 24 divided by 24 has a remainder of 0.25 divided by 24 has a remainder of 1.26 divided by 24 has a remainder of 2.pattern.therefore, 24+7=31 divided by 24 has a remainder of 7.31 + 24 gets you another number that, when you divide by 24, has a remainder of 7. you're adding on one whole 24.(while 7 divided by 24 has a remainder of 7, the question wants something greater than 7.)list of natural numbers that when divided by 24 has a remainder of 7 (add 24 each time):     31, 55, 79, 103, 127, 32 + 7 = 39 divided by 32 has remainder of 7the next number that when divided by 32 gives back a remainder of 7 is 39+32=71list of natural numbers that when divided by 32 has a remainder of 7 (add 32 each time):     39, 71, 103stop. 103 is the common number of both lists, and it's the first common number.