Trigonometric Functions and Applications

The video tutorial covers solving geometric and trigonometric problems. It begins with finding the radius of a circle using a given point and its equation. The tutorial then introduces basic trigonometry concepts using the mnemonic SOHCAHTOA, explaining sine, cosine, and tangent. It applies these concepts to solve various trigonometric problems, including calculating unknown side lengths in right triangles.

What is the radius of a circle if the point (-3, 2) lies on it and the equation is (x + 3)^2 + (y + 1)^2 = r^2?

• 2

• 4

• 1

• 3

If the sine of angle x is 5/13, what is the cosine of x?

• 13/5

• 5/12

• 5/13

• 12/13

If the sine of angle x is 5/13, what is the tangent of x?

• 13/5

• 12/5

• 5/13

• 5/12

Given that sine of angle A is 0.7 and the opposite side is 21, what is the length of the hypotenuse?

• 30

• 15

• 10

• 21

If the sine of angle A is 0.7, what is the length of side AC if the opposite side is 21?

• 30

• 21

• 15

• 10

If the tangent of 40 degrees is 0.84, what is the height of a street light if the adjacent side is 20 feet?

• 16.8 feet

• 15 feet

• 20 feet

• 18 feet

Which trigonometric function should be used to find the side BC in a right triangle if angle A is 32 degrees and the adjacent side is 8.2?

• Sine

• Secant

• Cosine

• Tangent

If angle A is 32 degrees in a right triangle, what is the correct equation for side BC using tangent?

• tan(32) = 10.6/BC

• tan(32) = BC/10.6

• tan(32) = 8.2/BC

• tan(32) = BC/8.2

In a right triangle, if angle B is 58 degrees, what is the tangent of angle B?

• 8.2/BC

• BC/8.2

• 10.6/BC

• BC/10.6

What is the cosine of angle A if the adjacent side is 8.2 and the hypotenuse is 10.6?

• 8.2/10.6

• 10.6/8.2

• BC/8.2

• 8.2/BC