maths.free › Trigonometry › Trigonometric identities
Trigonometric identities
Pythagorean, double-angle and sum identities, verified by simplification.
Identities are equations true for every angle. The Pythagorean identity sin²x + cos²x = 1 is Pythagoras on the unit circle; the double-angle and sum formulas follow from it and rotation. To verify one, simplify the difference of the two sides to zero.
Gumagana halimbawa · simplify sin(x)^2 + cos(x)^2
Simplify sin(x)^2 + cos(x)^2
Hakbang-hakbang
- \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}
Start from the expression.
- 1
Simplify.
Ipahayag ang sagot
Ngayon ikaw Pumili ng isang problema, o i-type o gumuhit ng iyong sarili. Sa bawat hakbang, isang larawan, ang sagot na nakatago hanggang sa hilingin mo.
Ang isang libreng account ay nagdaragdag ng mga tala sa bawat aralin, isang tala ng kung ano ang iyong natapos, ang iyong mga nalulutas na problema sa isang lugar, at isang guro na maaari mong tanungin tungkol sa pahinang ito. Ang matematika mismo ay bukas sa lahat, naka-sign in o hindi.
Mag-sign Up Mag-loginMga simbolong ginagamit dito
I-tap ang anumang simbolo para sa buong kahulugan, isang larawan, at kung ano ang ibig sabihin ng bawat titik sa ito.
Paano: Trigonometric identities
- Start from the expression.
- Simplify.
Mga katanungan na tanong ng mga tao
Why radians instead of degrees?
A radian is the angle whose arc equals the radius, so it is a pure ratio rather than an arbitrary 1/360 of a turn. With radians the derivative of sin x is exactly cos x; with degrees a factor of π/180 appears everywhere.
Why does sin x = 1/2 have infinitely many solutions?
Sine repeats every full turn, and within one turn it reaches 1/2 twice (at π/6 and 5π/6). Add any whole number of turns to either and it is still true.
How do I remember the exact values?
Two triangles: the 45-45-90 with sides 1, 1, √2 and the 30-60-90 with sides 1, √3, 2. Every value for 30°, 45° and 60° is a ratio of those sides; symmetry gives the rest of the circle.
Higit pa sa Trigonometry
The unit circleTrigonometric equationsDegrees and radiansRight-triangle trigonometry (SOH-CAH-TOA)Law of sines and law of cosinesGraphs of sine, cosine and tangentInverse trigonometric functions