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B.Sc Mathematics Trigonometric Identities and Equations — practice questions

Explore 73 free Trigonometric Identities and Equations questions in B.Sc Mathematics Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Trigonometric Identities and Equations questions and exercises with answers

Showing questions 1–30 of 73.

Complete the Pythagorean identitiesRead the answer and worked solution →Match each identity familyRead the answer and worked solution →Sort each function: even or oddRead the answer and worked solution →Flip and match the double-angle pairsRead the answer and worked solution →Order the steps to solve a trig quadraticRead the answer and worked solution →True or false: trig identitiesRead the answer and worked solution →Spot the expression that does not fitRead the answer and worked solution →Find the wrong piece in each formulaRead the answer and worked solution →Spot the false trigonometry claimRead the answer and worked solution →The Pythagorean identities of trigonometry are built on the properties of which figure?Read the answer and worked solution →What do the even-odd identities relate?Read the answer and worked solution →Among the six trigonometric functions, which two are even?Read the answer and worked solution →Which equation is one of the two quotient identities?Read the answer and worked solution →The reciprocal and quotient identities are derived from what?Read the answer and worked solution →If factoring and substitution both fail while verifying an identity, what is the recommended fallback?Read the answer and worked solution →Rewrite 4 cos^2 x - 1 using the difference of squares.Read the answer and worked solution →Write 25 - 9 sin^2 x as a product using the difference of squares.Read the answer and worked solution →Verifying (sec^2 x - 1) / sec^2 x = sin^2 x by splitting the fraction gives which intermediate expression?Read the answer and worked solution →Which expansion is the sum formula for cosine?Read the answer and worked solution →Using the difference formula, find the exact value of cos(5 pi / 4 - pi / 6).Read the answer and worked solution →Expand sin(a + b) with the sum formula for sine.Read the answer and worked solution →Evaluate sin(45 degrees - 30 degrees) exactly using the difference formula for sine.Read the answer and worked solution →Given cos a = 1/2 with a between 0 and pi, and sin b = 3/5 with b between -pi/2 and pi/2, find sin(a + b).Read the answer and worked solution →How is the sum formula for tangent obtained?Read the answer and worked solution →Which quotient is the difference formula for tangent?Read the answer and worked solution →With tan(pi/6) = 1 / sqrt(3) and tan(pi/4) = 1, find the exact value of tan(pi/6 + pi/4).Read the answer and worked solution →Given sin a = 3/5 with a in quadrant I and cos b = -5/13 with b in quadrant III, find sin(a + b).Read the answer and worked solution →Write tan(pi/9) in terms of its cofunction.Read the answer and worked solution →A wire meets a pole 47 feet up and a second wire meets it 40 feet up, both anchored 50 feet from the pole. What angle separates the wires?Read the answer and worked solution →Which expression equals sin(2x)?Read the answer and worked solution →

Worked practice questions

Complete the Pythagorean identities

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Missing parts
  1. Answer
    1
    Choices
    1. 0
    2. 1
    3. 2
  2. Answer
    sec^2 x
    Choices
    1. csc^2 x
    2. tan^2 x
    3. sec^2 x
  3. Answer
    csc^2 x
    Choices
    1. csc^2 x
    2. sec^2 x
    3. cot^2 x
Complete the statement
sin^2 x + cos^2 x = {0} 1 + tan^2 x = {1} 1 + cot^2 x = {2}
Instructions
Tap a chip to fill each blank so all three identities hold.
_Source: OpenStax Algebra and Trigonometry, section 9.1 Solving Trigonometric Equations with Identities_

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Match each identity family

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Matching pairs
  1. Left
    Pythagorean
    Right
    Built on right triangle properties
  2. Left
    Even-odd
    Right
    Relates an angle to its negative
  3. Left
    Reciprocal
    Right
    Pairs a function with its reciprocal
  4. Left
    Quotient
    Right
    Writes tan and cot as ratios
  5. Left
    Double-angle
    Right
    Sum formulas with both angles equal
  6. Left
    Half-angle
    Right
    Values for an angle cut in half
Instructions
Tap a name on the left, then tap the description that fits it.
_Source: OpenStax Algebra and Trigonometry, section 9.3 Double-Angle, Half-Angle, and Reduction Formulas_

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Sort each function: even or odd

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Left
Even
Items
  1. Item
    cos x
    Answer
    Even
  2. Item
    sec x
    Answer
    Even
  3. Item
    sin x
    Answer
    Odd
  4. Item
    tan x
    Answer
    Odd
  5. Item
    cot x
    Answer
    Odd
  6. Item
    csc x
    Answer
    Odd
Right
Odd
Instructions
Swipe left for an even function, right for an odd function.
_Source: OpenStax Algebra and Trigonometry, section 9.1 Solving Trigonometric Equations with Identities_

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