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Introduction to Trigonometry

Short Answer Type

111. Express the following in terms of trigonometric ratios of angles lying between 0° and 45°
sin 89° + tan 89°

107 Views

112. Express the following in terms of trigonometric ratios of angles lying between 0° and 45°
cosec 69° + cot 69°

110 Views

113. Express the following in terms of trigonometric ratios of angles lying between 0° and 45°
cos 75° + cot 75°

98 Views

114. Express the following in terms of trigonometric ratios of angles lying between 0° and 45°
cos 70° + cot 70°

94 Views

Long Answer Type

115. In ΔABC, right angled at c,if

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find the value of sinA. cosB + cosA. sinB

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116. If ∠ZB and ∠Q are acute angles such that sin B = sin Q, then prove that ∠B = ∠Q.

125 Views

Short Answer Type

117. In ΔABC right angled at A, given ∠B = 30°, AC = 3 cm. Find AB, BC and ∠ACB.

Given: ∠B = 30°, ∠A = 90° and AC = 3 cm

increment ABC comma

angle straight A plus angle straight B plus angle straight C space equals space 180 degree

rightwards double arrow space space space 90 degree plus 30 degree plus angle straight C space equals space 180 degree rightwards double arrow space space space space 120 degree space plus space angle straight C space equals space 180 degree rightwards double arrow space space space space space space space space space space space space space space space space space space angle straight C space equals space 60 degree

Now,

space space tan space 30 degree space equals space AC over AB

rightwards double arrow

fraction numerator 1 over denominator square root of 3 end fraction equals 3 over AB

rightwards double arrow

AB space equals space 3 square root of 3 space cm

and

sin space 30 degree space equals space AC over BC

rightwards double arrow space space space space space space space space space space space 1 half space equals space 3 over BC rightwards double arrow space space space space space space space space space space space BC space equals space 6 space cm space Hence comma space space space space space angle straight C space equals space 60 degree comma space space AB space equals space 3 square root of 3 space cm comma and space space space space space space space space space space space space space BC space equals space 6 space cm.

87 Views

118. Find the value of sin 30° geometrically.

1665 Views

119. Find the value of tan 60°, geometrically.

1831 Views

120.

If $sin thin space left parenthesis straight A minus straight B right parenthesis space equals space 1 half comma space space space space space cos space left parenthesis straight A plus straight B right parenthesis space equals space 1 half comma space space space 0 degree less than straight A plus straight B less or equal than 90 degree comma space space straight A greater than straight B.$ Find A and B.

82 Views