IB Mathematics Analysis and Approaches Topic AHL 3.9—reciprocal Trig Ratios and Their Pythagorean Identities. Inverse Circular Functions Questionbank (HL)

IB Mathematics Analysis and Approaches Topic AHL 3.9—reciprocal Trig Ratios and Their Pythagorean Identities. Inverse Circular Functions Questionbank (HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic AHL 3.9—reciprocal Trig Ratios and Their Pythagorean Identities. Inverse Circular Functions with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 3.9—reciprocal Trig Ratios and Their Pythagorean Identities. Inverse Circular Functions and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

HLPaper 2

Solve $sec^{2} x - 4 tan x = 4$ for $0 \leq x \leq 2 π$ .

[6]

Question 2

HLPaper 1

Consider the function $f (x) = sec x + tan (2 x)$ , where $x$ is in the domain of $f$ .

Show that the roots of the equation $f (x) = 0$ satisfy the equation $2 sin^{3} x + 2 sin^{2} x - 2 sin x - 1 = 0$

[4]

Show that $f (π - x) + f (π + x) = - 2 sec x$

[3]

Question 3

HLPaper 1

Prove that $tan (arcsin (x)) = \frac{x}{1 - x ^{2}}$ for $|x| < 1$ .

[4]

Question 4

HLPaper 1

Consider the function $f (x) = csc x + tan (2 x)$

Show that the roots of the equation $f (x) = 0$ satisfy the equation $2 cos^{3} x - 2 cos^{2} x - 2 cos x + 1 = 0$

[4]

Show that $f (π - x) + f (π + x) = 0$

[3]

Question 5

HLPaper 1

A point $P$ moves around the unit circle centered at the origin $O (0, 0)$ with coordinates $P (cos θ, sin θ)$ .

At a certain instant, the $x$ -coordinate of $P$ is $\frac{1}{5}$ . Find all possible values of $sin θ$ at that instant.

[2]

If $P$ lies in the first quadrant, find the exact values of $sin (2 θ)$ , $cos (2 θ)$ , and $tan (2 θ)$ .

[4]

Verify that the identity $1 + tan^{2} (2 θ) = sec^{2} (2 θ)$ holds for your values.

[2]

For $0 \leq θ < 2 π$ , a quantity $Q$ is defined by $Q = (3 sin θ - 3 cos θ)^{2}$ . Determine the maximum and minimum possible values of $Q$ , giving exact values.

[3]

Hence find the range of $θ$ (in radians, $0 \leq θ < 2 π$ ) for which the quantity $Q$ is greater than $4.5$ .

[3]

IB Mathematics Analysis and Approaches AHL 3.9—reciprocal Trig Ratios and Their Pythagorean Identities. Inverse Circular Functions Questionbank

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IB Mathematics Analysis and Approaches AHL 3.9—reciprocal Trig Ratios and Their Pythagorean Identities. Inverse Circular Functions Questionbank

IB Mathematics Analysis and Approaches (AA) Topic AHL 3.9—reciprocal Trig Ratios and Their Pythagorean Identities. Inverse Circular Functions Questionbank

Unlock all 24 questions with a free account