特殊三角形 ACB11√245°45°45∘, 45∘, 90∘\displaystyle 45^\circ,\ 45^\circ,\ 90^\circ45∘, 45∘, 90∘ACB√31230°60°30∘, 60∘, 90∘\displaystyle 30^\circ,\ 60^\circ,\ 90^\circ30∘, 60∘, 90∘ 知识测验 重做题目cos(π4)\displaystyle \cos\left(\dfrac\pi4\right)cos(4π) 的值是哪一个？A12\displaystyle \dfrac1221B22\displaystyle \dfrac{\sqrt2}222C32\displaystyle \dfrac{\sqrt3}223D2\displaystyle \sqrt22 三角恒等式 定理三角恒等式sin2(θ)+cos2(θ)=1sin(−θ)=−sin(θ)cos(−θ)=cos(θ)tan(θ)=sin(θ)cos(θ)cot(θ)=cos(θ)sin(θ)tan2(θ)+1=sec2(θ)cot2(θ)+1=csc2(θ)sin(θ)=cos(θ−π2)sin(a±b)=sin(a)cos(b)±cos(a)sin(b)cos(a±b)=cos(a)cos(b)∓sin(a)sin(b)sin(2θ)=2sin(θ)cos(θ)cos(2θ)=cos2(θ)−sin2(θ)sin2(θ)=1−cos(2θ)2cos2(θ)=1+cos(2θ)2\begin{aligned} & \sin^2(\theta) + \cos^2(\theta) = 1 \\[0.65em] & \sin(-\theta) = -\sin(\theta) \\[0.65em] & \cos(-\theta) = \cos(\theta) \\[0.65em] & \tan(\theta) = {\dfrac{\sin(\theta)}{\cos(\theta)}} \\[0.65em] & \cot(\theta) = {\dfrac{\cos(\theta)}{\sin(\theta)}} \\[0.65em] & \tan^2(\theta) + 1 = \sec^2(\theta) \\[0.65em] & \cot^2(\theta) + 1 = \csc^2(\theta) \\[0.65em] & \sin(\theta) = \cos\left(\theta - {\dfrac{\pi}{2}}\right) \\[0.65em] & \sin(a \pm b) = \sin(a)\cos(b) \pm \cos(a)\sin(b) \\[0.65em] & \cos(a \pm b) = \cos(a)\cos(b) \mp \sin(a)\sin(b) \\[0.65em] & \sin(2\theta) = 2\sin(\theta)\cos(\theta) \\[0.65em] & \cos(2\theta) = \cos^2(\theta) - \sin^2(\theta) \\[0.65em] & \sin^2(\theta) = {\dfrac{1 - \cos(2\theta)}{2}} \\[0.65em] & \cos^2(\theta) = {\dfrac{1 + \cos(2\theta)}{2}} \end{aligned}sin2(θ)+cos2(θ)=1sin(−θ)=−sin(θ)cos(−θ)=cos(θ)tan(θ)=cos(θ)sin(θ)cot(θ)=sin(θ)cos(θ)tan2(θ)+1=sec2(θ)cot2(θ)+1=csc2(θ)sin(θ)=cos(θ−2π)sin(a±b)=sin(a)cos(b)±cos(a)sin(b)cos(a±b)=cos(a)cos(b)∓sin(a)sin(b)sin(2θ)=2sin(θ)cos(θ)cos(2θ)=cos2(θ)−sin2(θ)sin2(θ)=21−cos(2θ)cos2(θ)=21+cos(2θ) 提醒：trign(x)trig^n(x)trign(x) 通常表示 (trig(x))n(trig(x))^n(trig(x))n。 这些恒等式在两边都有定义的地方成立。 知识测验 重做题目哪个等式对任意实数 θ\displaystyle \thetaθ 都成立？Acos(−θ)=−cos(θ)\displaystyle \cos(-\theta)=-\cos(\theta)cos(−θ)=−cos(θ)Bsin(−θ)=sin(θ)\displaystyle \sin(-\theta)=\sin(\theta)sin(−θ)=sin(θ)Ccos(−θ)=cos(θ)\displaystyle \cos(-\theta)=\cos(\theta)cos(−θ)=cos(θ)Dsin2(θ)+cos2(θ)=2\displaystyle \sin^2(\theta)+\cos^2(\theta)=2sin2(θ)+cos2(θ)=2 动手练习特殊角的三角函数值简单·5 分钟查看参考答案计算下列各式。(a) sin(π/4)\displaystyle \sin(\pi/4)sin(π/4)(b) cos(π/4)\displaystyle \cos(\pi/4)cos(π/4)(c) csc(π/4)\displaystyle \csc(\pi/4)csc(π/4) 动手练习三角方程的全部解中等·5 分钟查看参考答案求满足下列条件的所有 θ\displaystyle \thetaθ。(a) tan(θ)=1/3\displaystyle \tan(\theta)=1/\sqrt{3}tan(θ)=1/3(b) sec(θ)=2\displaystyle \sec(\theta)=\sqrt{2}sec(θ)=2(c) cot(θ)=3\displaystyle \cot(\theta)=\sqrt{3}cot(θ)=3
