Help Solve for Two Angles
Level 5
Trig Triumph Game Trigonometry Help
Show Minutes and Seconds as Digits after the Decimal Point.
Level 5 Find Two Angles
requires two answers for each question.
First use the calculator to determine Angle α then tap the button labeled
Answer A
. Your answer then displays on the
button. Second calculate Angle β, then tap the
button labeled Answer B
.
If you're not happy with your answers, then simply recalculate
and tap the Answer buttons.
When you're satisfied with both answers, tap the
Final Answer
button.
Calculate Two Angles
This Web page demonstrates how to solve for two angles, given the lengths of two sides of a right triangle,
Inverse Trigonometric Functions
The Ratios level demonstrated the trigonometric ratios sine, cosine, tangent, cosecant, secant, and cotangent.
For each trigonometric function there's an inverse trigonometric function. Inverse trigonmetric functions receive an input and return an output. Input the Trigonmetric Ratios from level two. Inverse trigonometric functions output an angle in degrees. In other words provide a trigonometric ratio to an inverse trigonometric function, to find the associated angle.
Find Two Angles Given Two Sides of a Right Triangle
Example 1
Given a right triangle where the lengths of the vertical and horizontal sides are both 1. The hypotenuse is 1.414.
We know the hypotenuse because:
c = √(12 + 12).. 1.414 ≈ √(1 + 1)
The sin of 1.414 would be 1/1.414 ≈ 0.707
The arcsin(0.707) ≈ 45.
Therefore both angles are 450.
Example 2
Given a triangle with hypotenuse 17" and side a
is 15".
The Sin of A is 15/17. 15/17 ≈ 0.882. asin(0.882) ≈ 61.880.
Therefore the angle A
is approximately 61.880.
Compositional Inverse
The terms compositional inverse and multiplicative inverse represent different operations. It's easy to become confused regarding the term inverse. A multiplicative inverse is the reciprocal of a fraction. For example, the multiplicative inverse of 1/2 is 2/1.
The inverse trigonometric functions are compositional inverses
not multiplicative inverses. A compositional or functional inverse,
reverses the effect of another function.
For example, assume angle A
equals 600. Sin of 600 equals approximately 0.866.
Asin (arcsine) of 0.866 is approximately 600.
In simpler terms, if the sin of y = x then the arcsin of x = y.
Look at Example 2 above, we can see that the Sin of 61.88 ≈ 0.882. The arcsin of 0.882 ≈ 61.880
Inverse trigonometric function output is restricted to provide only one possible solution.
Notation For the Game
The inverse trigonometric functions may be represented with different notations,
depending on the text or instructor.
For example the inverse function for Sin may be noted as
arcsin
, Sin-1, INV Sin, or asin.
The Trig Triumph
game uses the notation listed in the table above
for the set of inverse trigonometric functions.
The inverse trigonometric functions include
asin,
acos,
atan,
acsc,
asec, and
acot.
Scoring
Each question includes two answers, one answer for each angle. Receive 50 points for each correct angle. Receive 100 points if you answer both angles correctly for each question.
Level 5 includes 10 questions. Each question's maximum points equals 100. Receive a maximum of 500 points if you answer every angle in every question correctly.
Post Your Score Online
Select the Post Score
button to post your score online.
See how your score compares to others in the Trig Triumph Hall of Fame.
Rounding Errors
Trig Triumph rounds the final
answer to the nearest thousandth (3 digits after the decimal point).
The Trig Triumph game allows for small rounding differences.
The game rounds to the nearest three digits, and displays
the output, after you tap the Final Answer
button.
Often rounding each step in a series introduces rounding errors.
The final result may be too high, when more than one step in the series rounds up.
The final result may be too low, when more than one step in the series rounds down.
Therefore it's best to avoid rounding until the final answer. Let Trig Triumph
then
round the final answer.
Reset Level Five
Select the Reset
button at the bottom of the page, to
begin this level again. Reset
allows you to play the
level over again and increase your score. Reset
assigns zero to
your score for this level, then displays the first question for this level.
Trigonometry Help
Read short trigonometry tutorials.
Each tutorial also leads to a level of the Trig Triumph
game.
Play the game level to learn the section while
also having a little fun.
Trigonometry helps programmers, engineers, scientists, teachers, and students. Trigonometry provides a foundation with mathematics required for game programming, science, technology, engineering, and math (STEM).
Love learning trigonometry with tutorials, games and graphics!
