Evaluating the Six Trigonometric Functions
Which Pythagorean identity is correct?
tan² (0) + 1 = sec² (0)
The point P (x , y) lies on the terminal side of an angle 0 = 3π/4 in standard position. What are the signs of the values of x and y?
X is negative and Y is positive.
The point P (x, y) lies on the terminal side of an angle 0 = -60 degrees in standard position. What are the signs of the values of x and y?
X is positive and Y is negative.
Keisha and David found the same value for cos 0, as shown below, given sin 0 = -8/17. Whose procedure is correct?
Both procedures are correct.
The point P (x , y) is on the terminal Ray of angle 0. If 0 is between π radians and 3π/2 radians and csc 0 = -5/2, what are the coordinates of P (x , y)?
P (-√21 , -2)
Based on Pythagorean identities, which equation is true?
sec² 0 - tan² 0 = -1 (wrong) -cos² 0 - 1 = - sin ² 0 (wrong)
If cos 0 = 0.3090, which of the following represents approximate values of sin 0 and tan 0, for zero degrees < 0 < 90 degrees?
Sin 0 = 0.9511, tan 0 = 3.0780
Three trigonometric functions for a given angle are shown below. csc 0 = 13/12 , sec 0 = -13/5 , cot = -5/12 What are the coordinates of point (x , y) on the terminal Ray of angle 0, assuming that the values above were not simplified?
(-5, 12)
Given that sec 0 = -37/12, what is the value of cot 0 for π/2 < 0 < π?
-12/35
Given that tan 0 = -1, what is the value of sec 0, for 3π/2 < 0 < 2π?
-√2 (wrong)
If sin 0 = -0.7660, which of the following represents an approximate value of tan o for 180 degrees < 0 < 270 degrees?
1.1916
Given that sin 0 = 21/29 , what is the value of cos 0 for zero degrees < 0 < 90 degrees?
20/29
If a vertical line is dropped from the x axis to the point (12 , -9) in the diagram below, what is the value of sec 0?
5/4
Francesca drew point (-2 , -10) on the terminal Ray of angle 0, which is in standard position. She found values for the six trigonometric functions using the steps below. Which of the following explains whether all of Francesca's work is correct?
She made her first error in step 3 because the sine, cosine, and tangent ratios are incorrect, which also results in incorrect cosecant, secant, and tangent functions.
The terminal side of an angle in standard position passes through P (15 , -8). What is the value of sin 0?
Sin 0 = -8/17
The terminal side of an angle in standard position passes through P (-3 , -4). What is the value of tan 0?
Tan 0 = 4/3
Consider the relationship below, given π/2 < 0 < π. Sin² 0 + cos² 0 = 1 Which of the following best explains how this relationship and the value of sin 0 can be used to find the other trigonometric values?
The values of sin 0 and cos 0 represent the legs of a right triangle with a hypotenuse of 1, therefore, solving for cos 0 finds the unknown leg, and then all other trigonometric values can be found.
The point (-√2/2 , √2/2) is the point at which the terminal Ray of angle 0 intersects the unit circle. What are the values for the cosine and cotangent functions for angle 0?
cos 0 = √2/2 , cot 0 = -1/2 (wrong) cos 0 = -√2/2 , cot 0 = -1/2 (wrong)
Given that tan² 0 = 3/8, what is the value of sec 0?
± √(11/8)
Given that sin 0 = ²¹/₂₉, what is the value of cos 0, for zero degrees < 0 < 90 degrees?
²⁰/₂₉