Triangle Trigonometry flashcards
50 practice cards drawn from the Triangle Trigonometry lessons. Tap a card to turn it over. Every answer is checked against the lesson it came from.
Read the Triangle Trigonometry lessons in full →
Which ratio is opposite over hypotenuse?
sine
from “Sine, Cosine and Tangent”
Which ratio is opposite over adjacent?
tangent
from “Sine, Cosine and Tangent”
What is cos 45°?
from “Exact Sine, Cosine and Tangent at 30, 45 and 60°”
What is tan 60°?
from “Exact Sine, Cosine and Tangent at 30, 45 and 60°”
cos 12° equals which sine?
sin 78°
from “Sine and Cosine of Complementary Angles”
cos 25° equals which sine?
sin 65°
from “Sine and Cosine of Complementary Angles”
A right triangle has hypotenuse 18 and an angle of 30°. How long is the opposite side?
9
from “Solving Right Triangles”
A right triangle has hypotenuse 16 and an angle of 30°. How long is the opposite side?
8
from “Solving Right Triangles”
. What is ?
30°
from “Finding an Angle from a Ratio”
The opposite side is 5 and the adjacent is 2. Which expression gives the angle?
from “Finding an Angle from a Ratio”
Standing 35 m away, the angle of elevation to the top is 30°. How tall is it?
from “Elevation and Depression”
From a cliff 49 m high, the angle of depression to a boat is 45°. How far out is it?
49 m
from “Elevation and Depression”
What is cos 150°?
from “Sine and Cosine of Angles Past 90 Degrees”
What is cos 120°?
−½
from “Sine and Cosine of Angles Past 90 Degrees”
Where does sin x reach its highest value between 0° and 360°?
90°
from “The Graphs of Sine and Cosine”
The sine wave repeats itself every…?
360°
from “The Graphs of Sine and Cosine”
Between 0° and 180°, where does tan x have no value?
90°
from “The Graph of Tangent”
Between 90° and 180°, tan x is…
negative
from “The Graph of Tangent”
What is the greatest value of y = 2 sin x + 7?
9
from “Amplitude and the Principal Axis”
What is the greatest value of y = 5 sin x + 6?
11
from “Amplitude and the Principal Axis”
How many whole waves does y = sin 5x draw between 0° and 360°?
5
from “The Period and Phase Shift of a Wave”
Which way does y = sin(x − 60°) slide?
60° right
from “The Period and Phase Shift of a Wave”
cos x = cos 80°. Which other angle below 360° agrees?
280°
from “Solving Simple Trigonometric Equations”
sin x = ½. One answer is 30°. What is the other between 0° and 360°?
150°
from “Solving Simple Trigonometric Equations”
−45°
from “The Principal Values of the Inverse Functions”
30°
from “The Principal Values of the Inverse Functions”
Solve for .
0°, 45°, 180°, 225°
from “Quadratic Equations in Sine, Cosine or Tangent”
Solve for .
60°, 300°
from “Quadratic Equations in Sine, Cosine or Tangent”
Solve sin 2x = ½ for .
15°, 75°, 195°, 255°
from “Trigonometric Equations with a Multiple Angle”
Solve sin 3x = 0 for .
0°, 60°, 120°, 180°
from “Trigonometric Equations with a Multiple Angle”
A tide is d = 5 + 3 sin(30t)° with t in hours. How long from one high tide to the next?
12 hours
from “Modeling Tides and Daylight with a Sine Function”
A tide is d = 5 + 3 sin(30t)°. When in the first 6 hours is the depth 6.5 meters?
t = 1 and t = 5
from “Modeling Tides and Daylight with a Sine Function”
Two sides are 2 and 6, with 30° between them. What is the area?
3
from “Area with Sine”
Two sides are 3 and 4, with 30° between them. What is the area?
3
from “Area with Sine”
Side 12 faces 30°, and another angle is 45°. How long is the side facing 45°?
from “The Sine Rule”
Side 7 faces 30°, and another angle is 45°. How long is the side facing 45°?
from “The Sine Rule”
Two sides are 8 and 6, with 60° between them. What is the third side squared?
52
from “The Cosine Rule”
Sides 5 and 3 hold the angle C, and the side facing C is 7. What is cos C?
−½
from “The Cosine Rule”
Side 7 faces 30°, and a side of faces the angle B. What is B?
45°
from “Finding Angles with the Sine Rule”
Side 8 faces 30°, and a side of faces the angle B. What is B?
45°
from “Finding Angles with the Sine Rule”
sin B = ½. Which two angles are the candidates for B?
30° and 150°
from “The Ambiguous Case of the Sine Rule”
names which pair of candidates?
60° and 120°
from “The Ambiguous Case of the Sine Rule”
A triangle has sides 3 and 5 around the angle C, and 7 facing it. What is C?
120°
from “Finding Angles with the Cosine Rule”
A triangle has sides 5 and 8 around the angle C, and 7 facing it. What is C?
60°
from “Finding Angles with the Cosine Rule”
Which three sides make the flat triangle holding that angle?
floor diagonal, height, space diagonal
from “Trigonometry in Three Dimensions”
A floor measures 6 by 8. How long is its diagonal?
10
from “Trigonometry in Three Dimensions”
The hypotenuse is 14 and the angle is 45°. What is the opposite side, exactly?
from “Exact Trigonometric Ratios with Surds”
The hypotenuse is 12 and the angle is 45°. What is the opposite side, exactly?
from “Exact Trigonometric Ratios with Surds”
A ship sails 15 km on bearing 050°, then 7 km on 170°. How far is it back to A?
13 km
from “Bearings with the Sine and Cosine Rules”
A ship sails 7 km on bearing 060°, then 8 km on 120°. How far is it back to A?
13 km
from “Bearings with the Sine and Cosine Rules”