Math 4 Honors Final Exam

Front

What is the relationship between sine and cosine on the unit circle?

Back

On the unit circle, the y-coordinate represents the sine value (y = sin(x)), and the x-coordinate represents the cosine value (x = cos(x)).

Front

What is the measure of the missing angle if the other angles in a triangle are 45° and 90°?

Back

The measure of the missing angle is 45°.

Front

How do you determine the measure of an angle in a triangle when given two angles?

Back

To find the measure of the missing angle, subtract the sum of the known angles from 180°.

Front

Simplify the expression: 3i(4 - i) + i(6 + 2i)

Back

The simplified expression is 1 + 18i.

Front

What is the value of x if the equation is x + 5 = 10?

Back

The value of x is 5.

Front

Define sine in terms of a right triangle.

Back

In a right triangle, sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

Front

Define cosine in terms of a right triangle.

Back

In a right triangle, cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (a² + b² = c²).

Front

What is the unit circle?

Back

The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane, used to define trigonometric functions.

Front

How do you find the sine and cosine of common angles (30°, 45°, 60°)?

Back

Sine and cosine values for common angles are: sin(30°) = 1/2, cos(30°) = √3/2; sin(45°) = √2/2, cos(45°) = √2/2; sin(60°) = √3/2, cos(60°) = 1/2.