What does the Pythagorean theorem state?
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.
What is the formula for the Pythagorean theorem?
a² + b² = c², where c is the length of the hypotenuse.
True or False: The Pythagorean theorem can be applied to all triangles.
False
In a right triangle, if one angle is 30 degrees, what are the sine, cosine, and tangent values?
sin(30°) = 0.5, cos(30°) = √3/2, tan(30°) = 1/√3
Fill in the blank: The sine of an angle is the ratio of the _____ to the hypotenuse.
opposite side
What is the cosine of 45 degrees?
√2/2
What is the tangent of 60 degrees?
√3
True or False: The cosine function is negative in the first quadrant.
False
In which quadrants is the sine function positive?
In the first and second quadrants.
What is the general rule for the signs of sine, cosine, and tangent in Quadrant III?
Sine is negative, cosine is negative, tangent is positive.
What is the value of tan(90 degrees)?
Undefined
Fill in the blank: The cosine of an angle is the ratio of the _____ to the hypotenuse.
adjacent side
What is the relationship between degrees and radians for a right angle?
A right angle is 90 degrees or π/2 radians.
What is the sine of 0 degrees?
0
What is the tangent of 45 degrees?
1
True or False: The sine function can only take values between -1 and 1.
True
In a right triangle, if one side measures 3 units and the hypotenuse measures 5 units, what is the length of the other side?
4 units
What is the cosine of 90 degrees?
0
What is the tangent of 30 degrees?
1/√3
Fill in the blank: The tangent function is the ratio of the _____ to the adjacent side.
opposite side
What is the sine of 180 degrees?
0
What is the cosine of 180 degrees?
-1
In a right triangle, if the lengths of the two legs are equal, what type of triangle is it?
Isosceles right triangle
What is the value of sin(90 degrees)?
1
