alleryThe identity $\sin^2\theta + \cos^2\theta$ equals:
- $\sec^2\theta$
- $2\sin\theta$
- 1
- 0
Show answer and solution
Correct answer: C. 1
The fundamental Pythagorean identity: sin²θ + cos²θ = 1.
AP Calculus AB Unit 3B: Implicit Differentiation and Inverse Functions — practice questions — page 3
Explore 97 free Unit 3B: Implicit Differentiation and Inverse Functions questions in AP Calculus AB Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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The identity $\sin^2\theta + \cos^2\theta$ equals:Read the answer and worked solution →The identity $1 + \tan^2\theta$ equals:Read the answer and worked solution →$\sin(90^\circ - \theta)$ equals:Read the answer and worked solution →The radian measure of $45^\circ$ is:Read the answer and worked solution →The period of the function $\sin x$ is:Read the answer and worked solution →In a circle of radius $r$, an arc of length $l$ subtends at the centre an angle (in radians) of:Read the answer and worked solution →One radian is approximately equal to:Read the answer and worked solution →In radian measure, $\pi$ radians equals:Read the answer and worked solution →The complex number i is defined by:Read the answer and worked solution →For the complex number z = 2 + 5i, Re z and Im z are:Read the answer and worked solution →The conjugate of the complex number z = 2 - 5i is:Read the answer and worked solution →If 4x + i(3x - y) = 3 + i(-6), then x and y are:Read the answer and worked solution →Compute (3 + 5i)(2 + 6i).Read the answer and worked solution →What is i^35?Read the answer and worked solution →The modulus |3 + i| equals:Read the answer and worked solution →The multiplicative inverse of z = 2 - 3i is:Read the answer and worked solution →Express (5 + √2 i)/(1 - √2 i) in the form a + ib.Read the answer and worked solution →Find the value of i^(-39).Read the answer and worked solution →Compute (5 - 3i)³.Read the answer and worked solution →If x + iy = (a + ib)/(a - ib), then x² + y² equals:Read the answer and worked solution →Identify the standard form of (-i)(2i)(-i/8)³.Read the answer and worked solution →Two real numbers or two algebraic expressions related by <, >, ≤ or ≥ form:Read the answer and worked solution →Which of the following is a STRICT inequality?Read the answer and worked solution →Solve 30x < 200 where x is a natural number. The solution set is:Read the answer and worked solution →Solve 5x - 3 < 3x + 1 where x is an integer.Read the answer and worked solution →Add the same number 5 to both sides of -4 ≤ -2. The result is:Read the answer and worked solution →Divide BOTH sides of -6x ≥ 24 by -3. Result:Read the answer and worked solution →Identify the linear inequality in TWO variables.Read the answer and worked solution →Solve -3x + 5 > 2 over real numbers.Read the answer and worked solution →Identify a QUADRATIC inequality (not a linear inequality).Read the answer and worked solution →
Worked practice questions
The identity $1 + \tan^2\theta$ equals:
- $1$
- $\sec^2\theta$
- $\cot^2\theta$
- $\csc^2\theta$
Show answer and solution
Correct answer: B. $\sec^2\theta$
Dividing sin²θ+cos²θ=1 by cos²θ gives tan²θ+1 = sec²θ.
$\sin(90^\circ - \theta)$ equals:
- $\cos\theta$
- $-\cos\theta$
- $\sin\theta$
- $\tan\theta$
Show answer and solution
Correct answer: A. $\cos\theta$
By the complementary-angle identity, sin(90°−θ) = cosθ.
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Practise Unit 3B: Implicit Differentiation and Inverse Functions →More Mathematics topics
Unit 3A: Chain Rule and Composite FunctionsUnit 1A3: Function Composition and InversesUnit 1A1: Relations, Functions and GraphsUnit 1A2: Trigonometric Functions & Inverse TrigUnit 2: Differentiation and Fundamental Derivative RulesUnit 6A: Indefinite Integrals & Fundamental TheoremUnit 1B3: Asymptotic Behavior and Infinite LimitsUnit 1B1: Limit Concepts and Graphical Limits