StudentAidUnit 7: Trigonometry — Exercise 7 1
10th Class Mathematics · Unit 7: Trigonometry
7.1.1.(i) Find the sign of sin 55°. (ii) Find the sign of cos 145°. (iii) Find the sign of tan 111°. (iv) Find the sign of sec 179°. (v) Find the sign of cosec 88°. (vi) Find the sign of cot 14°.
Given
(i) Angle
55^circ lies in Quadrant I
Result
(i) Sign
sin 55^circ = Positive
Given
(ii) Angle
145^circ lies in Quadrant II
Result
(ii) Sign
cos 145^circ = Negative
Given
(iii) Angle
111^circ lies in Quadrant II
Result
(iii) Sign
tan 111^circ = Negative
Given
(iv) Angle
179^circ lies in Quadrant II
Result
(iv) Sign
sec 179^circ = Negative
Given
(v) Angle
88^circ lies in Quadrant I
Result
(v) Sign
cosec 88^circ = Positive
Given
(vi) Angle
14^circ lies in Quadrant I
Result
(vi) Sign
cot 14^circ = Positive
7.1.2.(i) Fill in the blank: tan(180° − θ) = ___ (ii) Fill in the blank: sin(180° − θ) = ___ (iii) Fill in the blank: tan(90° + θ) = ___ (iv) Fill in the blank: cos(90° + θ) = ___ (v) Fill in the blank: cosec(180° − θ) = ___ (vi) Fill in the blank: sec(90° − θ) = ___
Formula
(i) Reduction formula
tan(180^circ-θ) = -tanθ
(ii) Reduction formula
sin(180^circ-θ) = sinθ
(iii) Reduction formula
tan(90^circ+θ) = -cotθ
(iv) Reduction formula
cos(90^circ+θ) = -sinθ
(v) Reduction formula
cosec(180^circ-θ) = cosec θ
(vi) Reduction formula
sec(90^circ-θ) = cosec θ
(i) -tanθ,quad (ii) sinθ,quad (iii) -cotθ,quad (iv) -sinθ,quad (v) cosec θ,quad (vi) cosec θ
7.1.3.(i) Without using calculator, find the exact value of sin 150°. (ii) Without using calculator, find the exact value of tan 150°. (iii) Without using calculator, find the exact value of sec 150°. (iv) Without using calculator, find the exact value of cosec 120°. (v) Without using calculator, find the exact value of cos 120°. (vi) Without using calculator, find the exact value of cot 120°. (vii) Without using calculator, find the exact value of sin 135°. (viii) Without using calculator, find the exact value of sec 135°. (ix) Without using calculator, find the exact value of cot 135°.
Formula
(i)
sin 150^circ = sin(180^circ-30^circ) = sin 30^circ
Result
(i)
sin 150^circ = 12
Formula
(ii)
tan 150^circ = tan(180^circ-30^circ) = -tan 30^circ
Result
(ii)
tan 150^circ = -frac{1}{sqrt{3}
Formula
(iii)
sec 150^circ = sec(180^circ-30^circ) = -sec 30^circ
Result
(iii)
sec 150^circ = -frac{2}{sqrt{3}
Formula
(iv)
cosec 120^circ = cosec(180^circ-60^circ) = cosec 60^circ
Result
(iv)
cosec 120^circ = frac{2}{sqrt{3}
Formula
(v)
cos 120^circ = cos(180^circ-60^circ) = -cos 60^circ
Result
(v)
cos 120^circ = -12
Formula
(vi)
cot 120^circ = cot(180^circ-60^circ) = -cot 60^circ
Result
(vi)
cot 120^circ = -frac{1}{sqrt{3}
Formula
(vii)
sin 135^circ = sin(180^circ-45^circ) = sin 45^circ
Result
(vii)
sin 135^circ = frac{1}{sqrt{2}
Formula
(viii)
sec 135^circ = sec(180^circ-45^circ) = -sec 45^circ
Result
(viii)
sec 135^circ = -sqrt{2}
Formula
(ix)
cot 135^circ = cot(180^circ-45^circ) = -cot 45^circ
Result
(ix)
cot 135^circ = -1