Draw the Triangle
Part of the Trig Equations and Inverses section of Coddy's Trigonometry journey. Lesson 15 of 56.
To find cos(arcsin(3/5)), give the inner angle a name: θ = arcsin(3/5). Then sin(θ) = 3/5, and since 3/5 is positive, θ is between 0° and 90°: it is an angle of a right triangle with opposite side 3 and hypotenuse 5.
Pythagoras gives the third side: 3² + b² = 5², so b = 4. Now read the outer function off the triangle: cos(θ) = 4/5, so cos(arcsin(3/5)) = 4/5. No calculator, and the angle itself is never needed.
Challenge
θ = arcsin(5/13), and the board shows its triangle: opposite 5, hypotenuse 13. Find the third side x: tap the three sides, name the rule, solve, and press Check.
Try it yourself
Use the figure to find x
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Trig Equations and Inverses
1Your First Trig Equations
One Equation, Two AnglesReading Signs on the CircleThe Reference AngleRecap: First Equations4Compositions
Draw the TriangleThe Outer FunctionA Negative InsideWhen Undoing Does Not UndoRecap: Compositions2Inverses and Their Ranges
Why arcsin Gives One AngleNegative Inputs to arcsinThe Range of arccosThe Range of arctanRecap: Inverse Ranges5Equations on a Domain
A Negative CosineTangent EquationsEquations in RadiansTwo Turns, Four AnswersRecap: On a Domain