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Introduction to Trigonometry

Multiple Choice Questions

351.

The value of $fraction numerator 5 space sin squared 30 degree plus cos squared 45 degree plus 4 space tan squared space 60 degree over denominator 2 space sin space 30 degree space cos space 60 degree space plus space tan space 45 degree end fraction$ is

$9 1 over 6$
$8 1 fifth$
$5 2 over 6$
$5 2 over 6$

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352. If cos (40° + x) = sin 30° the value of x is

30°
40°
20°
20°

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353.

If $sinθ space equals space 3 over 5 comma space find space the space value space of space left parenthesis tan space straight theta space plus space sec space straight theta right parenthesis 2.$

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354. If 3 tan θ = 4, find the value of $fraction numerator 5 space sin space straight theta minus 3 cosθ over denominator 5 space sinθ plus 2 space cosθ end fraction$
$11 over 26$
$26 over 11$
$12 over 25$
$12 over 25$

11 over 26

fraction numerator 5 space sinθ minus 3 space cosθ over denominator 5 space sinθ space plus 2 space cosθ end fraction equals fraction numerator 5 begin display style sinθ over cosθ end style minus 3 begin display style cosθ over cosθ end style over denominator 5 begin display style sinθ over sinθ end style plus 2 begin display style cosθ over cosθ end style end fraction space rightwards double arrow space space fraction numerator 5 space tanθ minus 3 over denominator 5 space tanθ plus 2 end fraction equals fraction numerator 5 cross times begin display style 4 over 3 end style minus 3 over denominator 5 cross times begin display style 4 over 3 end style plus 2 end fraction equals fraction numerator 20 minus 9 over denominator 20 plus 6 end fraction equals 11 over 26

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355. Without using trigonometric tables, evaluate:

2 fraction numerator sin space 43 degree over denominator cos space 47 degree end fraction minus fraction numerator cot space 30 degree over denominator tan space 60 degree end fraction minus square root of 2 space sin space 45 degree

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356. Without using trigonometric tables, evaluate:

fraction numerator cos squared 20 degree plus cos squared 70 degree over denominator sin squared 59 degree plus sin squared 31 degree end fraction

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357. The value of : sin (50° + 0) - cos (40° - 0) is

2
1
-1
-1

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358.

The value of: $fraction numerator cot space 40 degree over denominator tan space 50 degree end fraction minus 1 half open parentheses fraction numerator cos space 35 degree over denominator sin space 55 degree end fraction close parentheses$ is

$1 half$
$negative 1 half$
$2 over 3$
$2 over 3$

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359.

Evaluate: $fraction numerator secθ. cosec left parenthesis 90 degree minus straight theta right parenthesis minus tanθ space cot left parenthesis 90 degree minus straight theta right parenthesis plus sin squared 55 degree space plus space sin squared 35 degree over denominator tan space 10 degree space tan space 20 degree space tan space 60 degree space tan space 70 degree space tan space 80 degree end fraction$