Cosecant, Secant, Cotangent
Part of the Right-Triangle Trigonometry section of Coddy's Trigonometry journey. Lesson 40 of 50.
Turn each of the three ratios upside down and you get three more: the same two sides, the other way up.
csc θ = 1/sin θ = hypotenuse / opposite
sec θ = 1/cos θ = hypotenuse / adjacent
cot θ = 1/tan θ = adjacent / opposite
In an 8, 15, 17 triangle with θ opposite the 8: sin θ = 8/17, so csc(theta) = 17/8; cos θ = 15/17, so sec θ = 17/15; tan θ = 8/15, so cot θ = 15/8. The pairing is the one trap: the co names cross over, so cosecant goes with sine and secant with cosine.
An equation with a reciprocal is solved by flipping it. csc(theta) = 17/8 is the same as sin(theta) = 8/17, and the board's chip Use arccsc: every angle in the domain does the flip and the arcsin in one step.
Challenge
In a right triangle, the cosecant of the acute angle θ is 25/7. Find θ in degrees, to two decimal places. Then press Check.
Try it yourself
Solve for theta
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Right-Triangle Trigonometry
1Sides of a Right Triangle
How Tall Is the Tree?The HypotenuseThe Opposite SideThe Adjacent SideWhen the Angle MovesRecap: Naming the Sides2The Three Ratios
The Sine RatioThe Cosine RatioThe Tangent RatioChoosing the RatioRecap: The Three Ratios5Finding an Angle
Inverse SineInverse CosineInverse TangentThe Angle of a RampBoth Acute AnglesRecap: Finding an Angle8Reciprocal Ratios
Cosecant, Secant, CotangentExact Reciprocal ValuesA Side From a CosecantA Ladder and a SecantRecap: Reciprocal Ratios