MathLab with Mr. Ahmed

MathLab with Mr. Ahmed is a math learning website by Ahmed Amasha, a mathematics teacher teaching the American curriculum. Explore Algebra 2, Precalculus, Calculus, and SAT and PSAT Math Prep through lessons, focused practice and printable resources.

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6.4 Inverse Trigonometric Functions and Right Triangles

Focus on inverse cosine and right triangle angle.

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Ideas in this lesson

Explore the lesson brief and the worked example for Idea 11. Create a free account to continue with the remaining ideas and practice.

01Evaluating inverse trig functions in degreesWorked steps · five questions02Finding angles in right trianglesWorked steps · five questions03Exact values of compositionsWorked steps · five questions
Lesson brief and rules

6.4 Inverse Trigonometric Functions and Right Triangles

An inverse trig function recovers the principal angle from a valid ratio.

Worked example 11
01 / For an acute angle with adjacent/hypotenuse =48=\dfrac{4}{8}, find θ\theta .
02 / cos⁡θ=12\cos \theta =\dfrac{1}{2}; its acute principal angle is π3\dfrac{\pi }{3}.
03 / Answer: π3\dfrac{\pi }{3}
Worked example 2 · Right triangle angle

A right triangle has opposite and adjacent sides both 44. What is its acute angle?

tan⁡θ=44=1\tan \theta =\dfrac{4}{4}=1, so θ=45∘\theta =45^{\circ}. Answer: 45∘45^{\circ}

15 questions covering every idea, with a worked answer for each.Start practice ↗
Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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