AQA · Mathematics · 8300

GCSE Maths: Trigonometry: Tangent graph

Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Trigonometry: Tangent graph (Corbettmaths Video 340), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.

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  1. What is the range of possible values for sin(x)?

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    Between -1 and 1 (inclusive). The sine of an angle cannot be less than -1 or greater than 1.

  2. What is the range of possible values for cos(x)?

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    Between -1 and 1 (inclusive). The cosine of an angle cannot be less than -1 or greater than 1.

  3. At what x-coordinate does y = sin(x) reach its maximum point in the interval 180° ≤ x ≤ 540°?

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    270°. The maximum value of sin(x) is 1, which occurs at 270° in that interval.

  4. At what x-coordinate does y = sin(x) reach its minimum point in the interval 360° ≤ x ≤ 720°?

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    450°. The minimum value of sin(x) is -1, which occurs at 450° in that interval.

  5. At what x-coordinate does y = cos(x) reach its minimum point in the interval 360° ≤ x ≤ 720°?

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    540°. The minimum value of cos(x) is -1, which occurs at 540° in that interval.

  6. If cos(x) = 0.766 and one solution is x = 40°, what is the other solution for 0° ≤ x ≤ 360°?

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    x = 320°. Cosine is symmetric about x = 180°, so the other solution is 360° - 40° = 320°.

  7. If sin(x) = -0.5 and one solution is x = 210°, what is the other solution for 0° ≤ x ≤ 360°?

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    x = 330°. For negative sine values, both solutions are in the third and fourth quadrants.

  8. For an acute angle x, is tan(x) positive, negative, or zero?

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    Positive (tan x > 0). In the first quadrant (acute angles), tangent is always positive.

  9. For an angle x where 270° < x < 360°, what are the signs of tan(x) and cos(x)?

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    tan(x) < 0 and cos(x) > 0. In the fourth quadrant, tangent is negative and cosine is positive.

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