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First Year Math Fundamentals of Trigonometry


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Class 9Class 10First YearSecond Year
1.Findthesignsofthefollowingtrigonometricfunctions.(x)sin34π1. Find the signs of the following trigonometric functions.(x) \sin \frac{3}{4} \pi

Q.43 1-\sec ^{2} \theta= is equal to(a) \tan ^{2} \theta (b) -\tan ^{2} \theta (c) \tan ^{2} \theta-1 (d) 1-\tan ^{2} \theta
Q.43  1-\sec ^{2} \theta=  is equal to(a)  \tan ^{2} \theta (b)  -\tan ^{2} \theta (c)  \tan ^{2} \theta-1 (d)  1-\tan ^{2} \theta

Q.431sec2θ=isequalto(a)tan2θ(b)tan2θ(c)tan2θ1(d)1tan2θQ.43 1-\sec ^{2} \theta= is equal to(a) \tan ^{2} \theta (b) -\tan ^{2} \theta (c) \tan ^{2} \theta-1 (d) 1-\tan ^{2} \theta

1. Verify the following:(iii) 2 \sin 45^{\circ}+\frac{1}{2} \operatorname{cosec} 45^{\circ}=\frac{3}{\sqrt{2}}
1. Verify the following:(iii)  2 \sin 45^{\circ}+\frac{1}{2} \operatorname{cosec} 45^{\circ}=\frac{3}{\sqrt{2}}

1.Verifythefollowing:(iii)2sin45+12cosec45=321. Verify the following:(iii) 2 \sin 45^{\circ}+\frac{1}{2} \operatorname{cosec} 45^{\circ}=\frac{3}{\sqrt{2}}

2. Evaluate the following:ii) \frac{1-\tan ^{2} \frac{\pi}{3}}{1+\tan ^{2} \frac{\pi}{3}}
2. Evaluate the following:ii)  \frac{1-\tan ^{2} \frac{\pi}{3}}{1+\tan ^{2} \frac{\pi}{3}}

2.Evaluatethefollowing:ii)1tan2π31+tan2π32. Evaluate the following:ii) \frac{1-\tan ^{2} \frac{\pi}{3}}{1+\tan ^{2} \frac{\pi}{3}}

Q.21 80^{\circ}= (a) \frac{5 \pi}{6} radians (b) \frac{4 \pi}{9} radians (c) \frac{\pi}{4} radians(d) 180 \pi radians
Q.21  80^{\circ}= (a)  \frac{5 \pi}{6}  radians (b)  \frac{4 \pi}{9}  radians (c)  \frac{\pi}{4}  radians(d)  180 \pi  radians

Q.2180=(a)5π6radians(b)4π9radians(c)π4radians(d)180πradiansQ.21 80^{\circ}= (a) \frac{5 \pi}{6} radians (b) \frac{4 \pi}{9} radians (c) \frac{\pi}{4} radians(d) 180 \pi radians

Evaluate:1. \sin \frac{\pi}{3} \cos \frac{\pi}{6}-\cos \frac{\pi}{3} \sin \frac{\pi}{6}
Evaluate:1.  \sin \frac{\pi}{3} \cos \frac{\pi}{6}-\cos \frac{\pi}{3} \sin \frac{\pi}{6}

Evaluate:1.sinπ3cosπ6cosπ3sinπ6Evaluate:1. \sin \frac{\pi}{3} \cos \frac{\pi}{6}-\cos \frac{\pi}{3} \sin \frac{\pi}{6}

1. Find the signs of the following trigonometric functions.(v) \tan 299^{\circ}
1. Find the signs of the following trigonometric functions.(v)  \tan 299^{\circ}

1.Findthesignsofthefollowingtrigonometricfunctions.(v)tan2991. Find the signs of the following trigonometric functions.(v) \tan 299^{\circ}

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