Free Printable formule goniometriche

1.

$sen\left(\frac{\pi}{2}-\alpha\right)=?$

a)

$sen\alpha$

b)

$\cos\alpha$

c)

$-sen\alpha$

d)

$-\cos\alpha$

2.

tg(-x)

a)

cotgx

b)

-cotgx

c)

tgx

d)

-tgx

3.

Quale delle seguenti NON è vera:

a)

$\cos\left(2\alpha\right)=1-2\sin^2\alpha$

b)

$\sin\left(2\alpha\right)=2\sin\alpha\cos\alpha$

c)

$\cos\left(2\alpha\right)=\sin^2\alpha-\cos^2\alpha$

d)

$\cos\left(2\alpha\right)=2\cos^2\alpha-1$

4.

$\sin\alpha\cos\beta-\cos\alpha\sin\beta=$

a)

$\sin\left(\alpha+\beta\right)$

b)

$\cos\left(\alpha+\beta\right)$

c)

$\sin\left(\alpha-\beta\right)$

d)

$\cos\left(\alpha-\beta\right)$

5.

$\cos\ \frac{\alpha}{2}$

a)

+/- $\sqrt[3]{\frac{1+\cos\alpha}{2}}$

b)

+ $\sqrt[2]{\frac{1-\cos\alpha}{2}}$

c)

+/- $\sqrt[2]{\frac{1+\cos^2\alpha}{2}}$

d)

+/- $\sqrt[2]{\frac{1+\cos\alpha}{2}}$

6.

$\sin\ \left(\alpha-\beta\right)$

a)

$\sin\alpha\cdot\cos\beta+\cos\alpha\cdot\sin\beta$

b)

$\sin\alpha\cdot\cos\beta-\sin\beta\cdot\cos\alpha$

c)

$\cos\alpha\cdot\sin\beta-\cos\beta\cdot\sin\alpha$

d)

$\cos\alpha\cdot\cos\beta-\sin\alpha\cdot\sin\beta$

7.

$\cos\ \left(30\degree+45\degree\right)$

a)

$\frac{\sqrt[2]{6}+\sqrt[2]{2}}{4}$

b)

0,25

c)

$\frac{\sqrt[2]{4}}{4}$

d)

$\frac{\sqrt[2]{6}-\sqrt[2]{2}}{4}$

8.

$\cos\alpha=\frac{1}{2}$

$tg\ \frac{\alpha}{2}=?$

a)

$\frac{1}{2}$

b)

$\frac{\sqrt[2]{3}}{2}$

c)

$\frac{3}{\sqrt[2]{3}}$

d)

0,577

9.

$\sin\alpha=\frac{\sqrt[2]{3}}{2}$

$\cos2\alpha=?$

a)

$-\frac{1}{2}$

b)

$-2^{-1}$

c)

$\frac{\sqrt[2]{3}}{2}$

d)

$-\frac{\sqrt[2]{3}}{2}$

10.

$tg\left(30°-45°\right)$

a)

$\sqrt[2]{3}-2$

b)

$\sqrt[2]{3}$

c)

$\frac{\sqrt[2]{3}}{3}$

d)

$\frac{1}{2}$

11.

Usa le formule di duplicazione per trovare il valore di $\sin\left(2\theta\right)$ sapendo che cos θ = 4/5 e che 270° < θ < 360°

a)

$-\frac{1}{5}$

b)

$\frac{24}{25}$

c)

$-\frac{24}{25}$

d)

$-\frac{25}{24}$

12.

$\sin5B\sin B$

a)

$\frac{\cos4B-\cos6B}{2}$

b)

$\frac{\sin4B+\cos6B}{2}$

c)

$\frac{\sin6B+\sin4B}{2}$

d)

$\frac{\cos4B-\sin6B}{2}$

13.

sin(100°)cos(1°)+cos(100°)sin(1°)

a)

cos(101°)

b)

cos(99°)

c)

sin(101°)

d)

cos(99°)

14.

cos(100°)cos(1°)+sin(100°)sin(1°)

a)

cos(101°)

b)

sin(99°)

c)

sin(101°)

d)

cos(99°)

15.

cos(20)cos(40) - sin(20)sin(40)=

a)

1/4

b)

1/2

c)

√(3)/2

d)

√(3)

16.

Se tan α = 3/4 e tan β = (-1/2)
allora tan (α-β)=?

a)

(-10√5)/25

b)

(-2√5)/25

c)

(√2-√6)/4

d)

2

17.

$2\cos\left(\frac{1}{4}\pi+x\right)\sin\left(\frac{1}{4}\pi+x\right)$ equivalent with...

a)

$1-\sin2x$

b)

$1-\cos2x$

c)

$1+\sin2x$

d)

$1+\cos2x$

e)

$\cos2x$

18.

Se semplifichi la seguente espressione: $\cos2\alpha\ -\ \frac{\cos\alpha\ \sin2\alpha}{\sin\alpha}$ ottieni come risultato..

a)

$-1$

b)

$1$

c)

$0$

19.

Completa la formula di duplicazione: $\cos2\theta\ =$ ...

a)

$\cos^2\alpha-\sin^2\alpha$

b)

$\cos^2\theta-\sin^2\theta$

c)

$2\sin\theta\cos\theta$

d)

$2\sin\alpha\cos\alpha$

20.

Semplificando l'espressione $\sin2\alpha\ +\cos2\alpha-2\sqrt[]{2}\cos\alpha\ \sin\left(\alpha+\frac{\pi}{4}\right)$ ottieni come risultato

a)

-1

b)

+1

c)

0

21.

Quale delle seguenti funzioni ha il grafico della figura accanto?

a)

$y=2\sin\left(2x\right)$

b)

$y=2\cos\left(2x\right)$

c)

$y=2\sin\left(\frac{x}{2}\right)$

d)

$y=2\cos\left(\frac{x}{2}\right)$

22.

$\cos\left(\alpha+\beta\right)\cdot\cos\left(\alpha-\beta\right)=$

a)

$\cos^2\beta+\cos^2\alpha$

b)

$\cos^2\beta-\cos^2\alpha$

c)

$\cos^2\beta-\sin^2\alpha$

d)

$\cos^2\beta+\sin^2\alpha$

23.

$\sin\left(\alpha+\frac{\pi}{3}\right)=$

a)

$\cos\left(\frac{\pi}{6}-\alpha\right)$

b)

$\cos\left(\frac{\pi}{6}+\alpha\right)$

c)

$sen\left(\frac{\pi}{6}+\alpha\right)$

d)

$\cos\left(\frac{\pi}{2}+\alpha\right)$

24.

$\cos2\alpha+\sin2\alpha+2\sin^2\alpha=$

a)

$\cos^2\alpha$

b)

$\sin^2\alpha$

c)

$\left(\cos\alpha+\sin\alpha\right)^2$

d)

$\left(\cos\alpha-\sin\alpha\right)^2$

formule goniometriche

Total questions: 24

Worksheet time: 48mins

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