Question

Find the sine, cosine, and tangent of 45 degrees.

A) Sin 45 degrees = negative square root of 2 divided by 2, cos 45 degrees = negative square root of 2 divided by 2, tan 45 degrees = negative square root of 2

B) Sin 45 degrees = square root of 2 divided by 2, cos 45 degrees = square root of 2 divided by 2, tan 45 degrees = square root of 2

C) Sin 45 degrees = square root of 2 divided by 2, cos 45 degrees = square root of 2 divided by 2, tan 45 degrees = 1

D) Sin 45 degrees = square root of 2 divided by 2, cos 45 degrees = square root of 2 divided by 2, tan 45 degrees = −1

Answer 1

The sine, cosine, and tangent of 45 degrees can be found using the values of the adjacent side, opposite side, and hypotenuse of a right triangle. The sine of 45 degrees is (√2) / 2, the cosine is (√2) / 2, and the tangent is 1.

Step-by-step explanation:

The sine, cosine, and tangent of 45 degrees can be found using the values of the adjacent side, opposite side, and hypotenuse of a right triangle. In this case, for a 45-degree angle, the adjacent side and opposite side are equal, so we can use the Pythagorean theorem to find the value of the hypotenuse. Let's denote the length of the adjacent and opposite sides as x.

Sine (sin) 45 degrees: sin 45 degrees = opposite side / hypotenuse = x / √2x = 1 / √2 = (√2) / 2

Cosine (cos) 45 degrees: cos 45 degrees = adjacent side / hypotenuse = x / √2x = 1 / √2 = (√2) / 2

Tangent (tan) 45 degrees: tan 45 degrees = opposite side / adjacent side = x / x = 1

Answer 2

The correct answer is option C.

Sin 45 degrees = square root of 2 divided by 2, cos 45 degrees = square root of 2 divided by 2, tan 45 degrees = 1

Step-by-step explanation:

The sin cos tan table used to calculate values of the ratios for different angles can be used for the values.

The table is easily available on the internet.

WE can use a a right-angles isosceles triangle to find the exact values for the angle 45.

The equal sides have length 1. So the thirs side using the pythagoras theorem will be √2.

So

Sin 45 = √2/2

Cos 45 = √2/2

and

Tan 45 = 1

So the correct option is C.