Question

Знайдіть tga, якщо sina=3/4 ,90⁰

Answer 1

Ответ:

Если угол α<90°:

\displaystyle tg\alpha=\frac{\sin\alpha}{\cos\alpha} =\frac{\sin\alpha}{\sqrt{1-\sin^2\alpha} } =\frac{4}{5\sqrt{1-\frac{16}{25} } } =\frac{4}{5\sqrt{\frac{9}{25} } }=\frac{4}{5\cdot\frac{3}{5} } = \frac{4\cdot5}{3\cdot5} =\frac{4}{3}tgα=

cosα

sinα

=

1−sin

2

α

sinα

=

5

1−

25

16

4

=

5

25

9

4

=

5⋅

5

3

4

=

3⋅5

4⋅5

=

3

4

2. Если угол α>90°:

\displaystyle tg\alpha=\frac{\sin\alpha}{\cos\alpha}=\frac{\sin(180^\circ-\alpha)}{\cos(180^\circ-\alpha)}=\frac{\sin\alpha}{-\cos\alpha}=\frac{\sin\alpha}{-\sqrt{1-\sin^2\alpha}}=-\frac{4}{5\cdot\sqrt{1-\frac{16}{25}}} =-\frac{4}{5\cdot\sqrt{\frac{9}{25}}}=-\frac{4}{5\cdot\frac{3}{5}} =-\frac{4\cdot5}{3\cdot5}=-\frac{4}{3}tgα=

cosα

sinα

=

cos(180

∘

−α)

sin(180

∘

−α)

=

−cosα

sinα

=

−

1−sin

2

α

sinα

=−

5⋅

1−

25

16

4

=−

5⋅

25

9

4

=−

5⋅

5

3

4

=−

3⋅5

4⋅5

=−

3

4